https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/api.php?action=feedcontributions&user=Boj44979&feedformat=atomHigher Invariants - User contributions [en]2021-06-17T05:04:32ZUser contributionsMediaWiki 1.19.10https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-06-02T20:35:17Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in spring/summer 2021==<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | April 27<br />
| style="width:300px;" | [https://www.maths.ox.ac.uk/people/guillem.cazassus Guillem Cazassus] (Oxford)<br />
| style="width:400px;" | The earring correspondence of the pillowcase<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_cazassus.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6088610d13d905.94167507 Video]<br />
| style="width:600px;" | Singular instanton homology is a knot invariant introduced by Kronheimer and Mrowka. It is deeply tied to Khovanov homology, and among other things, permits to show that the latter detects the unknot.<br />
<br />
In order to compute singular instanton homology, Hedden, Herald and Kirk defined a symplectic (Atiyah-Floer) analogue, called pillowcase homology. This is a Lagrangian Floer homology in the traceless character variety of the four-punctured sphere.<br />
<br />
We study the Lagrangian correspondence induced by the earring tangle, an essential ingredient in Kronheimer-Mrowka's construction. Our computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties. This is joint work with Chris<br />
Herald, Paul Kirk and Artem Kotelskiy.<br />
|- style="vertical-align:top;"<br />
| May 4<br />
| [https://web.math.princeton.edu/~szabo/ Zoltán Szabó] (Princeton)<br />
| Knot Floer homology constructions and the Pong Algebra<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zoltan_szabo_slides_regensburg.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6092843f3ac1f2.55974595 Video]<br />
| In a joint work with Peter Ozsvath we have developed algebraic invariants for knots using a family of bordered knot algebras. The goal of this lecture is to review these constructions and discuss some of the latest developments<br />
|- style="vertical-align:top;"<br />
| May 11<br />
| [https://sites.google.com/bc.edu/john-baldwin/home John Baldwin] (Boston College)<br />
| Instanton L-spaces and splicing<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_john_baldwin.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/609b80d9ef1517.27795704 Video]<br />
| We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.<br />
|- style="vertical-align:top;"<br />
| May 18<br />
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)<br />
| Anchored foams and annular homology<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_akhmechet.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60a4b821c1f1a5.35673801 Video]<br />
| We describe equivariant sl(2) and sl(3) homology for links in the solid torus, identified with the thickened annulus, via foam evaluation and universal construction. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams that may intersect the distinguished line. Intersection points, called anchor points, contribute additional terms to the foam evaluation. State spaces and link homology carry additional gradings coming from anchor points. I will describe our evaluation formula and the resulting annular homology theories, as well as relations to other constructions. This is joint work with Mikhail Khovanov.<br />
|- style="vertical-align:top;"<br />
| May 25<br />
| ''no talk (whit tuesday)''<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 1<br />
|[https://people.mpim-bonn.mpg.de/aruray/ Arunima Ray] (MPIM Bonn)<br />
| A surface embedding theorem<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-ray.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60b73387b2e8b4.23924882 Video]<br />
| Generalising work of Freedman-Quinn and Stong from 30-40 years ago, we prove a surface embedding theorem for 4-manifolds with good fundamental group, in the presence of potentially unframed dual spheres. The essential obstruction is the Kervaire-Milnor invariant, and I will describe how to compute it and present some useful corollaries of the theorem. The goal of the talk is to be reasonably self-contained, and no prior expert knowledge of 4-manifold topology should be required. This is joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.<br />
|- style="vertical-align:top;"<br />
| June 8<br />
| [https://cns.utexas.edu/directory/item/353-gordon-cameron-m?Itemid=349 Cameron Gordon] (UT Austin)<br />
| Toroidal 3-manifolds and the properties in the L-space Conjecture<br />
| The L-space Conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an L-space (NLS), having left-orderable fundamental group (LO), and supporting a co-orientable taut foliation (CTF). We study these properties for toroidal 3-manifolds. For example, Eftekhary and Hanselman-Rasmussen-Watson have shown that toroidal homology spheres are NLS; we show that they are LO. We also show that the cyclic branched covers of a prime satellite knot are NLS and LO, and CTF if the companion is fibered. A partial extension to links allows us to show that a prime quasi-alternating link is either a (2,q) torus link or hyperbolic, generalizing Menasco's classical result for non-split alternating links. This is joint work with Steve Boyer and Ying Hu.<br />
|- style="vertical-align:top;"<br />
| June 15<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelmé] (Queen's University)<br />
| Hyperbolic-like actions on &#8477; and applications to (contact) Anosov flows<br />
| Say that an action of a group G on the real line is hyperbolic-like if it commutes with the integer translations and every element either has no fixed points or exactly one pair of attractor/repeller in [0,1).<br />
<br />
I will explain how knowing which elements of a hyperbolic-like action admit fixed points is enough to characterize the action up to conjugacy.<br />
<br />
Our goal behind this theorem was its application to the problem of classifying (&#8477;-covered) Anosov flows up to orbit equivalence, which I will explain. It also turns out that it yields an equivalence between contact Anosov flows up to orbit equivalence and contact structures up to isomorphism, allowing to directly use contact geometry to solve problems on Anosov flows and vice versa.<br />
<br />
This is joint work with Kathryn Mann and Jonathan Bowden.<br />
|- style="vertical-align:top;"<br />
| June 22<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 29<br />
| [https://www2.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (Notre Dame)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 6<br />
| [https://www.math.princeton.edu/people/jonathan-zung Jonathan Zung] (Princeton)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 13<br />
| [https://www.math.wustl.edu/~sfrankel/ Steven Frankel] (Washington University in St. Louis)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
<center><img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-06-02T20:34:11Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in spring/summer 2021==<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | April 27<br />
| style="width:300px;" | [https://www.maths.ox.ac.uk/people/guillem.cazassus Guillem Cazassus] (Oxford)<br />
| style="width:400px;" | The earring correspondence of the pillowcase<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_cazassus.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6088610d13d905.94167507 Video]<br />
| style="width:600px;" | Singular instanton homology is a knot invariant introduced by Kronheimer and Mrowka. It is deeply tied to Khovanov homology, and among other things, permits to show that the latter detects the unknot.<br />
<br />
In order to compute singular instanton homology, Hedden, Herald and Kirk defined a symplectic (Atiyah-Floer) analogue, called pillowcase homology. This is a Lagrangian Floer homology in the traceless character variety of the four-punctured sphere.<br />
<br />
We study the Lagrangian correspondence induced by the earring tangle, an essential ingredient in Kronheimer-Mrowka's construction. Our computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties. This is joint work with Chris<br />
Herald, Paul Kirk and Artem Kotelskiy.<br />
|- style="vertical-align:top;"<br />
| May 4<br />
| [https://web.math.princeton.edu/~szabo/ Zoltán Szabó] (Princeton)<br />
| Knot Floer homology constructions and the Pong Algebra<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zoltan_szabo_slides_regensburg.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6092843f3ac1f2.55974595 Video]<br />
| In a joint work with Peter Ozsvath we have developed algebraic invariants for knots using a family of bordered knot algebras. The goal of this lecture is to review these constructions and discuss some of the latest developments<br />
|- style="vertical-align:top;"<br />
| May 11<br />
| [https://sites.google.com/bc.edu/john-baldwin/home John Baldwin] (Boston College)<br />
| Instanton L-spaces and splicing<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_john_baldwin.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/609b80d9ef1517.27795704 Video]<br />
| We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.<br />
|- style="vertical-align:top;"<br />
| May 18<br />
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)<br />
| Anchored foams and annular homology<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_akhmechet.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60a4b821c1f1a5.35673801 Video]<br />
| We describe equivariant sl(2) and sl(3) homology for links in the solid torus, identified with the thickened annulus, via foam evaluation and universal construction. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams that may intersect the distinguished line. Intersection points, called anchor points, contribute additional terms to the foam evaluation. State spaces and link homology carry additional gradings coming from anchor points. I will describe our evaluation formula and the resulting annular homology theories, as well as relations to other constructions. This is joint work with Mikhail Khovanov.<br />
|- style="vertical-align:top;"<br />
| May 25<br />
| ''no talk (whit tuesday)''<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 1<br />
|[https://people.mpim-bonn.mpg.de/aruray/ Arunima Ray] (MPIM Bonn)<br />
| A surface embedding theorem<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-ray.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60b73387b2e8b4.23924882 Video]<br />
| Generalising work of Freedman-Quinn and Stong from 30-40 years ago, we prove a surface embedding theorem for 4-manifolds with good fundamental group, in the presence of potentially unframed dual spheres. The essential obstruction is the Kervaire-Milnor invariant, and I will describe how to compute it and present some useful corollaries of the theorem. The goal of the talk is to be reasonably self-contained, and no prior expert knowledge of 4-manifold topology should be required. This is joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.<br />
|- style="vertical-align:top;"<br />
| June 8<br />
| [https://cns.utexas.edu/directory/item/353-gordon-cameron-m?Itemid=349 Cameron Gordon] (UT Austin)<br />
| Toroidal 3-manifolds and the properties in the L-space Conjecture<br />
| The L-space Conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an L-space (NLS), having left-orderable fundamental group (LO), and supporting a co-orientable taut foliation (CTF). We study these properties for toroidal 3-manifolds. For example, Eftekhary and Hanselman-Rasmussen-Watson have shown that toroidal homology spheres are NLS; we show that they are LO. We also show that the cyclic branched covers of a prime satellite knot are NLS and LO, and CTF if the companion is fibered. A partial extension to links allows us to show that a prime quasi-alternating link is either a (2,q) torus link or hyperbolic, generalizing Menasco's classical result for non-split alternating links. This is joint work with Steve Boyer and Ying Hu.<br />
|- style="vertical-align:top;"<br />
| June 15<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelmé] (Queen's University)<br />
| Hyperbolic-like actions on R and applications to (contact) Anosov flows<br />
| Say that an action of a group G on the real line is hyperbolic-like if it commutes with the integer translations and every element either has no fixed points or exactly one pair of attractor/repeller in [0,1).<br />
<br />
I will explain how knowing which elements of a hyperbolic-like action admit fixed points is enough to characterize the action up to conjugacy.<br />
<br />
Our goal behind this theorem was its application to the problem of classifying (R-covered) Anosov flows up to orbit equivalence, which I will explain. It also turns out that it yields an equivalence between contact Anosov flows up to orbit equivalence and contact structures up to isomorphism, allowing to directly use contact geometry to solve problems on Anosov flows and vice versa.<br />
<br />
This is joint work with Kathryn Mann and Jonathan Bowden.<br />
|- style="vertical-align:top;"<br />
| June 22<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 29<br />
| [https://www2.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (Notre Dame)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 6<br />
| [https://www.math.princeton.edu/people/jonathan-zung Jonathan Zung] (Princeton)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 13<br />
| [https://www.math.wustl.edu/~sfrankel/ Steven Frankel] (Washington University in St. Louis)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
<center><img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-06-02T20:33:34Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in spring/summer 2021==<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | April 27<br />
| style="width:300px;" | [https://www.maths.ox.ac.uk/people/guillem.cazassus Guillem Cazassus] (Oxford)<br />
| style="width:400px;" | The earring correspondence of the pillowcase<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_cazassus.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6088610d13d905.94167507 Video]<br />
| style="width:600px;" | Singular instanton homology is a knot invariant introduced by Kronheimer and Mrowka. It is deeply tied to Khovanov homology, and among other things, permits to show that the latter detects the unknot.<br />
<br />
In order to compute singular instanton homology, Hedden, Herald and Kirk defined a symplectic (Atiyah-Floer) analogue, called pillowcase homology. This is a Lagrangian Floer homology in the traceless character variety of the four-punctured sphere.<br />
<br />
We study the Lagrangian correspondence induced by the earring tangle, an essential ingredient in Kronheimer-Mrowka's construction. Our computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties. This is joint work with Chris<br />
Herald, Paul Kirk and Artem Kotelskiy.<br />
|- style="vertical-align:top;"<br />
| May 4<br />
| [https://web.math.princeton.edu/~szabo/ Zoltán Szabó] (Princeton)<br />
| Knot Floer homology constructions and the Pong Algebra<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zoltan_szabo_slides_regensburg.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6092843f3ac1f2.55974595 Video]<br />
| In a joint work with Peter Ozsvath we have developed algebraic invariants for knots using a family of bordered knot algebras. The goal of this lecture is to review these constructions and discuss some of the latest developments<br />
|- style="vertical-align:top;"<br />
| May 11<br />
| [https://sites.google.com/bc.edu/john-baldwin/home John Baldwin] (Boston College)<br />
| Instanton L-spaces and splicing<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_john_baldwin.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/609b80d9ef1517.27795704 Video]<br />
| We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.<br />
|- style="vertical-align:top;"<br />
| May 18<br />
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)<br />
| Anchored foams and annular homology<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_akhmechet.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60a4b821c1f1a5.35673801 Video]<br />
| We describe equivariant sl(2) and sl(3) homology for links in the solid torus, identified with the thickened annulus, via foam evaluation and universal construction. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams that may intersect the distinguished line. Intersection points, called anchor points, contribute additional terms to the foam evaluation. State spaces and link homology carry additional gradings coming from anchor points. I will describe our evaluation formula and the resulting annular homology theories, as well as relations to other constructions. This is joint work with Mikhail Khovanov.<br />
|- style="vertical-align:top;"<br />
| May 25<br />
| ''no talk (whit tuesday)''<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 1<br />
|[https://people.mpim-bonn.mpg.de/aruray/ Arunima Ray] (MPIM Bonn)<br />
| A surface embedding theorem<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-ray.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60b73387b2e8b4.23924882 Video]<br />
| Generalising work of Freedman-Quinn and Stong from 30-40 years ago, we prove a surface embedding theorem for 4-manifolds with good fundamental group, in the presence of potentially unframed dual spheres. The essential obstruction is the Kervaire-Milnor invariant, and I will describe how to compute it and present some useful corollaries of the theorem. The goal of the talk is to be reasonably self-contained, and no prior expert knowledge of 4-manifold topology should be required. This is joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.<br />
|- style="vertical-align:top;"<br />
| June 8<br />
| [https://cns.utexas.edu/directory/item/353-gordon-cameron-m?Itemid=349 Cameron Gordon] (UT Austin)<br />
| Toroidal 3-manifolds and the properties in the L-space Conjecture<br />
| The L-space Conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an L-space (NLS), having left-orderable fundamental group (LO), and supporting a co-orientable taut foliation (CTF). We study these properties for toroidal 3-manifolds. For example, Eftekhary and Hanselman-Rasmussen-Watson have shown that toroidal homology spheres are NLS; we show that they are LO. We also show that the cyclic branched covers of a prime satellite knot are NLS and LO, and CTF if the companion is fibered. A partial extension to links allows us to show that a prime quasi-alternating link is either a (2,q) torus link or hyperbolic, generalizing Menasco's classical result for non-split alternating links. This is joint work with Steve Boyer and Ying Hu.<br />
|- style="vertical-align:top;"<br />
| June 15<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelmé] (Queen's University)<br />
| Hyperbolic-like actions on R and applications to (contact) Anosov flows<br />
| Say that an action of a group G on the real line is hyperbolic-like if it commutes with the integer translations and every element either has no fixed points or exactly one pair of attractor/repeller in [0,1).<br />
<br />
I will explain how knowing which elements of a hyperbolic-like action admit fixed points is enough to characterize the action up to conjugacy.<br />
<br />
Our goal behind this theorem was its application to the problem of classifying (R-covered) Anosov flows up to orbit equivalence, which I will explain. It also turns out that it yields an equivalence between contact Anosov flows up to orbit equivalence and contact structures up to isomorphism, allowing to directly use contact geometry to solve problems on Anosov flows and vice versa.<br />
|- style="vertical-align:top;"<br />
| June 22<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 29<br />
| [https://www2.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (Notre Dame)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 6<br />
| [https://www.math.princeton.edu/people/jonathan-zung Jonathan Zung] (Princeton)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 13<br />
| [https://www.math.wustl.edu/~sfrankel/ Steven Frankel] (Washington University in St. Louis)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
<center><img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-05-20T06:40:36Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in spring/summer 2021==<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | April 27<br />
| style="width:300px;" | [https://www.maths.ox.ac.uk/people/guillem.cazassus Guillem Cazassus] (Oxford)<br />
| style="width:400px;" | The earring correspondence of the pillowcase<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_cazassus.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6088610d13d905.94167507 Video]<br />
| style="width:600px;" | Singular instanton homology is a knot invariant introduced by Kronheimer and Mrowka. It is deeply tied to Khovanov homology, and among other things, permits to show that the latter detects the unknot.<br />
<br />
In order to compute singular instanton homology, Hedden, Herald and Kirk defined a symplectic (Atiyah-Floer) analogue, called pillowcase homology. This is a Lagrangian Floer homology in the traceless character variety of the four-punctured sphere.<br />
<br />
We study the Lagrangian correspondence induced by the earring tangle, an essential ingredient in Kronheimer-Mrowka's construction. Our computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties. This is joint work with Chris<br />
Herald, Paul Kirk and Artem Kotelskiy.<br />
|- style="vertical-align:top;"<br />
| May 4<br />
| [https://web.math.princeton.edu/~szabo/ Zoltán Szabó] (Princeton)<br />
| Knot Floer homology constructions and the Pong Algebra<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zoltan_szabo_slides_regensburg.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6092843f3ac1f2.55974595 Video]<br />
| In a joint work with Peter Ozsvath we have developed algebraic invariants for knots using a family of bordered knot algebras. The goal of this lecture is to review these constructions and discuss some of the latest developments<br />
|- style="vertical-align:top;"<br />
| May 11<br />
| [https://sites.google.com/bc.edu/john-baldwin/home John Baldwin] (Boston College)<br />
| Instanton L-spaces and splicing<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_john_baldwin.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/609b80d9ef1517.27795704 Video]<br />
| We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.<br />
|- style="vertical-align:top;"<br />
| May 18<br />
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)<br />
| Anchored foams and annular homology<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_akhmechet.pdf Slides]<br />
[https://mediathek2.uni-regensburg.de/playthis/60a4b821c1f1a5.35673801 Video]<br />
| We describe equivariant sl(2) and sl(3) homology for links in the solid torus, identified with the thickened annulus, via foam evaluation and universal construction. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams that may intersect the distinguished line. Intersection points, called anchor points, contribute additional terms to the foam evaluation. State spaces and link homology carry additional gradings coming from anchor points. I will describe our evaluation formula and the resulting annular homology theories, as well as relations to other constructions. This is joint work with Mikhail Khovanov.<br />
|- style="vertical-align:top;"<br />
| May 25<br />
| ''no talk (whit tuesday)''<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 1<br />
|[https://people.mpim-bonn.mpg.de/aruray/ Arunima Ray] (MPIM Bonn)<br />
| A surface embedding theorem<br />
| Generalising work of Freedman-Quinn and Stong from 30-40 years ago, we prove a surface embedding theorem for 4-manifolds with good fundamental group, in the presence of potentially unframed dual spheres. The essential obstruction is the Kervaire-Milnor invariant, and I will describe how to compute it and present some useful corollaries of the theorem. The goal of the talk is to be reasonably self-contained, and no prior expert knowledge of 4-manifold topology should be required. This is joint work with Daniel Kasprowski, Mark Powell, and Peter Teichner.<br />
|- style="vertical-align:top;"<br />
| June 8<br />
| [https://cns.utexas.edu/directory/item/353-gordon-cameron-m?Itemid=349 Cameron Gordon] (UT Austin)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 15<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelmé] (Queen's University)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 22<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 29<br />
| [https://www2.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (Notre Dame)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 6<br />
| [https://www.math.princeton.edu/people/jonathan-zung Jonathan Zung] (Princeton)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 13<br />
| [https://www.math.wustl.edu/~sfrankel/ Steven Frankel] (Washington University in St. Louis)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
<center><img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-05-03T13:04:59Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in spring/summer 2021==<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | April 27<br />
| style="width:300px;" | [https://www.maths.ox.ac.uk/people/guillem.cazassus Guillem Cazassus] (Oxford)<br />
| style="width:400px;" | The earring correspondence of the pillowcase<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_cazassus.pdf Slides] [https://mediathek2.uni-regensburg.de/playthis/6088610d13d905.94167507 Video]<br />
| style="width:600px;" | Singular instanton homology is a knot invariant introduced by Kronheimer and Mrowka. It is deeply tied to Khovanov homology, and among other things, permits to show that the latter detects the unknot.<br />
<br />
In order to compute singular instanton homology, Hedden, Herald and Kirk defined a symplectic (Atiyah-Floer) analogue, called pillowcase homology. This is a Lagrangian Floer homology in the traceless character variety of the four-punctured sphere.<br />
<br />
We study the Lagrangian correspondence induced by the earring tangle, an essential ingredient in Kronheimer-Mrowka's construction. Our computation suggests that figure eight bubbling — a subtle degeneration phenomenon predicted by Bottman and Wehrheim — appears in the context of traceless character varieties. This is joint work with Chris<br />
Herald, Paul Kirk and Artem Kotelskiy.<br />
|- style="vertical-align:top;"<br />
| May 4<br />
| [https://web.math.princeton.edu/~szabo/ Zoltán Szabó] (Princeton)<br />
| Knot Floer homology contructions and the Pong Algebra<br />
| In a joint work with Peter Ozsvath we have developed algebraic invariants for knots using a family of bordered knot algebras. The goal of this lecture is to review these constructions and discuss some of the latest developments<br />
|- style="vertical-align:top;"<br />
| May 11<br />
| [https://sites.google.com/bc.edu/john-baldwin/home John Baldwin] (Boston College)<br />
| Instanton L-spaces and splicing<br />
| We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert longitudes, cannot be an instanton L-space. This recovers the recent theorem of Lidman–Pinzon-Caicedo–Zentner that the fundamental group of every closed, oriented, toroidal 3-manifold admits a nontrivial SU(2)-representation, and consequently Zentner’s earlier result that the fundamental group of every closed, oriented 3-manifold besides the 3-sphere admits a nontrivial SL(2, C)-representation. This is joint work with Steven Sivek.<br />
|- style="vertical-align:top;"<br />
| May 18<br />
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| May 25<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 1<br />
|[https://people.mpim-bonn.mpg.de/aruray/ Arunima Ray] (MPIM Bonn)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 8<br />
| [https://cns.utexas.edu/directory/item/353-gordon-cameron-m?Itemid=349 Cameron Gordon] (UT Austin)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 15<br />
| [https://sites.google.com/site/thomasbarthelme/ Thomas Barthelmé] (Queen's University)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 22<br />
|<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 29<br />
| [https://www2.math.upenn.edu/~alkju/ Alexandra Kjuchukova] (Notre Dame)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 6<br />
| <br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| July 13<br />
| [https://www.math.wustl.edu/~sfrankel/ Steven Frankel] (Washington University in St. Louis)<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
<center><img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-02-09T20:28:58Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/robert-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fb4d2422f61b2.73706115 Video]<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/sdr_24_nov_2020.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fbd4068e33dc3.77710228 Video]<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
|Heegaard genus, degree-one maps, and amalgamation of 3-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides-rlgts.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fc8f3e3747153.83277089 Video]<br />
|Let $W$ be the exterior of a knot in a homology sphere and let $M$ be an amalgamation of $W$ and any other compact 3-manifold along boundary torus. Let $N$ be the manifold obtained by pinching $W$ into a solid torus. This means that there is a degree-one map from $M$ to $N$. We prove that the Heegaard genus of $M$ is at least as large as the Heegaard genus of $N$. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.<br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| Relative genus bounds in indefinite four-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-manolescu.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fcfb23dcafad9.40493309 Video]<br />
| Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X - B^4, with boundary a knot K. We give several methods to produce bounds on the genus of such surfaces in a fixed homology class. Our techniques include relative adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold. We give an example showing that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. Further, we give examples of knots that are topologically but not smoothly H-slice in some indefinite 4-manifolds. This is joint work with Marco Marengon and Lisa Piccirillo.<br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| Taut foliations and Dehn surgery along positive braid knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-krishna-2.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fda17e11a0472.19734089 Video]<br />
| The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of "positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.<br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| Morse-Bott theory on analytic spaces and applications to topology of smooth 4-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_feehan.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/60073d8a57fe92.43278551 Video]<br />
| We describe a new approach to Morse theory on singular analytic spaces of the kind that typically arise in gauge theory, such as the moduli space of SO(3) monopoles over 4-manifolds or the moduli space of Higgs pairs over Riemann surfaces. We explain how this new version of Morse theory, called virtual Morse-Bott theory, can potentially be used to answer questions arising in the geography of 4-manifolds, such as whether constraints on the topology of compact complex surfaces of general type continue to hold for symplectic 4-manifolds or even for smooth 4-manifolds of Seiberg-Witten simple type. This is joint work with Tom Leness.<br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| The diffeomorphism group of a 4-manifold<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_ruberman.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/60106744ab4e90.23857283 Video]<br />
| Associated to a smooth n-dimensional manifold are two infinite-dimensional groups: the group of homeomorphisms Homeo(M), and the group of diffeomorphisms, Diff(M). For manifolds of dimension greater than 4, the topology of these groups has been intensively studied since the 1950s. For instance, Milnor’s discovery of exotic 7-spheres immediately shows that there are distinct path components of the diffeomorphism group of the 6-sphere that are connected in its homeomorphism group. The lowest dimension for such classical phenomena is 5. <br />
<br />
I will discuss recent joint work with Dave Auckly about these groups in dimension 4. For each n, we construct a simply connected 4-manifold Z and an infinite subgroup of the nth homotopy group of Diff(Z) that lies in the kernel of the natural map to the corresponding homotopy group of Homeo(Z). These elements are detected by (n+1)-parameter gauge theory. The construction uses a topological technique.<br />
|- style="vertical-align:top;"<br />
| February 2<br />
| [https://www.i2m.univ-amu.fr/perso/luisa.paoluzzi/hple.html Luisa Paoluzzi] (University of Aix-Marseille)<br />
|Cyclic branched covers of alternating knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_paoluzzi.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/6019a543a4c668.36515602 Video]<br />
<br />
|The goal of the talk is to show that certain topological invariants of knots, called cyclic branched covers, are strong invariants for prime alternating knots. I will start by describing what cyclic branched covers are before presenting some known facts concerning their properties as invariants of knots. I will then point out what features of alternating knots are key to prove the result. The actual proof will be given in the second part of the talk. <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| [http://www.math.ubc.ca/~liam/ Liam Watson] (University of British Columbia)<br />
| Symmetry and mutation<br />
| Mutation is a relatively simple process for altering a knot in a non-trivial way, but it turns out to be quite tricky to see the difference between mutant pairs—a surprisingly wide range of knot invariants are unable to distinguish mutants. In the first part of the talk, I will give some background on the symmetry group associated with a knot, and show that this group is sometimes able to see mutation. In the second part of the talk, I will outline some work with Andrew Lobb, in which we appeal to a symmetry—when present—in order to define a refinement of Khovanov homology that is able to separate mutants.<br />
|- style="vertical-align:top;"<br />
| February 16<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>r-spin mapping class groups and applications</i><br />
| An r-spin structure on a surface can be thought of as a gadget for measuring “Z/rZ-valued winding numbers” of curves on the surface. There is an evident action of the mapping class group on the set of such objects; an r-spin mapping class group is the associated stabilizer. r-spin structures appear in a wide variety of contexts at the interface of topology and algebraic geometry: singularity theory, translation surfaces/Abelian differentials, linear systems on algebraic surfaces. I will explain what is now known about r-spin mapping class groups and the uses to which the theory can be put. This encompasses various projects with my collaborators Aaron Calderon and Pablo Portilla Cuadrado.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-01-25T22:28:26Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea/coffee/beer...).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/robert-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fb4d2422f61b2.73706115 Video]<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/sdr_24_nov_2020.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fbd4068e33dc3.77710228 Video]<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
|Heegaard genus, degree-one maps, and amalgamation of 3-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides-rlgts.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fc8f3e3747153.83277089 Video]<br />
|Let $W$ be the exterior of a knot in a homology sphere and let $M$ be an amalgamation of $W$ and any other compact 3-manifold along boundary torus. Let $N$ be the manifold obtained by pinching $W$ into a solid torus. This means that there is a degree-one map from $M$ to $N$. We prove that the Heegaard genus of $M$ is at least as large as the Heegaard genus of $N$. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.<br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| Relative genus bounds in indefinite four-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-manolescu.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fcfb23dcafad9.40493309 Video]<br />
| Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X - B^4, with boundary a knot K. We give several methods to produce bounds on the genus of such surfaces in a fixed homology class. Our techniques include relative adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold. We give an example showing that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. Further, we give examples of knots that are topologically but not smoothly H-slice in some indefinite 4-manifolds. This is joint work with Marco Marengon and Lisa Piccirillo.<br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| Taut foliations and Dehn surgery along positive braid knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-krishna-2.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fda17e11a0472.19734089 Video]<br />
| The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of "positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.<br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| Morse-Bott theory on analytic spaces and applications to topology of smooth 4-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides_feehan.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/60073d8a57fe92.43278551 Video]<br />
| We describe a new approach to Morse theory on singular analytic spaces of the kind that typically arise in gauge theory, such as the moduli space of SO(3) monopoles over 4-manifolds or the moduli space of Higgs pairs over Riemann surfaces. We explain how this new version of Morse theory, called virtual Morse-Bott theory, can potentially be used to answer questions arising in the geography of 4-manifolds, such as whether constraints on the topology of compact complex surfaces of general type continue to hold for symplectic 4-manifolds or even for smooth 4-manifolds of Seiberg-Witten simple type. This is joint work with Tom Leness.<br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| The diffeomorphism group of a 4-manifold<br />
| Associated to a smooth n-dimensional manifold are two infinite-dimensional groups: the group of homeomorphisms Homeo(M), and the group of diffeomorphisms, Diff(M). For manifolds of dimension greater than 4, the topology of these groups has been intensively studied since the 1950s. For instance, Milnor’s discovery of exotic 7-spheres immediately shows that there are distinct path components of the diffeomorphism group of the 6-sphere that are connected in its homeomorphism group. The lowest dimension for such classical phenomena is 5. <br />
<br />
I will discuss recent joint work with Dave Auckly about these groups in dimension 4. For each n, we construct a simply connected 4-manifold Z and an infinite subgroup of the nth homotopy group of Diff(Z) that lies in the kernel of the natural map to the corresponding homotopy group of Homeo(Z). These elements are detected by (n+1)-parameter gauge theory. The construction uses a topological technique.<br />
|- style="vertical-align:top;"<br />
| February 2<br />
| [https://www.i2m.univ-amu.fr/perso/luisa.paoluzzi/hple.html Luisa Paoluzzi] (University of Aix-Marseille)<br />
|Cyclic branched covers of alternating knots<br />
|The goal of the talk is to show that certain topological invariants of knots, called cyclic branched covers, are strong invariants for prime alternating knots. I will start by describing what cyclic branched covers are before presenting some known facts concerning their properties as invariants of knots. I will then point out what features of alternating knots are key to prove the result. The actual proof will be given in the second part of the talk. <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| [http://www.math.ubc.ca/~liam/ Liam Watson] (University of British Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| February 16<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-01-18T18:18:55Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/robert-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fb4d2422f61b2.73706115 Video]<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/sdr_24_nov_2020.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fbd4068e33dc3.77710228 Video]<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
|Heegaard genus, degree-one maps, and amalgamation of 3-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides-rlgts.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fc8f3e3747153.83277089 Video]<br />
|Let $W$ be the exterior of a knot in a homology sphere and let $M$ be an amalgamation of $W$ and any other compact 3-manifold along boundary torus. Let $N$ be the manifold obtained by pinching $W$ into a solid torus. This means that there is a degree-one map from $M$ to $N$. We prove that the Heegaard genus of $M$ is at least as large as the Heegaard genus of $N$. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.<br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| Relative genus bounds in indefinite four-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-manolescu.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fcfb23dcafad9.40493309 Video]<br />
| Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X - B^4, with boundary a knot K. We give several methods to produce bounds on the genus of such surfaces in a fixed homology class. Our techniques include relative adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold. We give an example showing that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. Further, we give examples of knots that are topologically but not smoothly H-slice in some indefinite 4-manifolds. This is joint work with Marco Marengon and Lisa Piccirillo.<br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| Taut foliations and Dehn surgery along positive braid knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-krishna-2.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fda17e11a0472.19734089 Video]<br />
| The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of "positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.<br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| Morse-Bott theory on analytic spaces and applications to topology of smooth 4-manifolds<br />
| We describe a new approach to Morse theory on singular analytic spaces of the kind that typically arise in gauge theory, such as the moduli space of SO(3) monopoles over 4-manifolds or the moduli space of Higgs pairs over Riemann surfaces. We explain how this new version of Morse theory, called virtual Morse-Bott theory, can potentially be used to answer questions arising in the geography of 4-manifolds, such as whether constraints on the topology of compact complex surfaces of general type continue to hold for symplectic 4-manifolds or even for smooth 4-manifolds of Seiberg-Witten simple type. This is joint work with Tom Leness.<br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| <i>The diffeomorphism group of a 4-manifold</i><br />
| Associated to a smooth n-dimensional manifold are two infinite-dimensional groups: the group of homeomorphisms Homeo(M), and the group of diffeomorphisms, Diff(M). For manifolds of dimension greater than 4, the topology of these groups has been intensively studied since the 1950s. For instance, Milnor’s discovery of exotic 7-spheres immediately shows that there are distinct path components of the diffeomorphism group of the 6-sphere that are connected in its homeomorphism group. The lowest dimension for such classical phenomena is 5. <br />
<br />
I will discuss recent joint work with Dave Auckly about these groups in dimension 4. For each n, we construct a simply connected 4-manifold Z and an infinite subgroup of the nth homotopy group of Diff(Z) that lies in the kernel of the natural map to the corresponding homotopy group of Homeo(Z). These elements are detected by (n+1)—parameter gauge theory. The construction uses a topological technique.<br />
|- style="vertical-align:top;"<br />
| February 2<br />
| [https://www.i2m.univ-amu.fr/perso/luisa.paoluzzi/hple.html Luisa Paoluzzi] (University of Aix-Marseille)<br />
|Cyclic branched covers of alternating knots<br />
|The goal of the talk is to show that certain topological invariants of knots, called cyclic branched covers, are strong invariants for prime alternating knots. I will start by describing what cyclic branched covers are before presenting some known facts concerning their properties as invariants of knots. I will then point out what features of alternating knots are key to prove the result. The actual proof will be given in the second part of the talk. <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| [http://www.math.ubc.ca/~liam/ Liam Watson] (University of British Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| February 16<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-01-07T14:28:59Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/robert-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fb4d2422f61b2.73706115 Video]<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/sdr_24_nov_2020.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fbd4068e33dc3.77710228 Video]<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
|Heegaard genus, degree-one maps, and amalgamation of 3-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides-rlgts.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fc8f3e3747153.83277089 Video]<br />
|Let $W$ be the exterior of a knot in a homology sphere and let $M$ be an amalgamation of $W$ and any other compact 3-manifold along boundary torus. Let $N$ be the manifold obtained by pinching $W$ into a solid torus. This means that there is a degree-one map from $M$ to $N$. We prove that the Heegaard genus of $M$ is at least as large as the Heegaard genus of $N$. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.<br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| Relative genus bounds in indefinite four-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-manolescu.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fcfb23dcafad9.40493309 Video]<br />
| Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X - B^4, with boundary a knot K. We give several methods to produce bounds on the genus of such surfaces in a fixed homology class. Our techniques include relative adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold. We give an example showing that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. Further, we give examples of knots that are topologically but not smoothly H-slice in some indefinite 4-manifolds. This is joint work with Marco Marengon and Lisa Piccirillo.<br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| Taut foliations and Dehn surgery along positive braid knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-krishna-2.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fda17e11a0472.19734089 Video]<br />
| The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of "positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.<br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| February 2<br />
| [https://www.i2m.univ-amu.fr/perso/luisa.paoluzzi/hple.html Luisa Paoluzzi] (University of Aix-Marseille)<br />
| tba<br />
| <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| [http://www.math.ubc.ca/~liam/ Liam Watson] (University of British Columbia)<br />
| tba<br />
| <br />
|- style="vertical-align:top;"<br />
| February 16<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2021-01-07T14:28:30Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/robert-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fb4d2422f61b2.73706115 Video]<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/sdr_24_nov_2020.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fbd4068e33dc3.77710228 Video]<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
|Heegaard genus, degree-one maps, and amalgamation of 3-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides-rlgts.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fc8f3e3747153.83277089 Video]<br />
|Let $W$ be the exterior of a knot in a homology sphere and let $M$ be an amalgamation of $W$ and any other compact 3-manifold along boundary torus. Let $N$ be the manifold obtained by pinching $W$ into a solid torus. This means that there is a degree-one map from $M$ to $N$. We prove that the Heegaard genus of $M$ is at least as large as the Heegaard genus of $N$. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.<br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| Relative genus bounds in indefinite four-manifolds<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-manolescu.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fcfb23dcafad9.40493309 Video]<br />
| Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X - B^4, with boundary a knot K. We give several methods to produce bounds on the genus of such surfaces in a fixed homology class. Our techniques include relative adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold. We give an example showing that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. Further, we give examples of knots that are topologically but not smoothly H-slice in some indefinite 4-manifolds. This is joint work with Marco Marengon and Lisa Piccirillo.<br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| Taut foliations and Dehn surgery along positive braid knots<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/slides-krishna-2.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fda17e11a0472.19734089 Video]<br />
| The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of "positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.<br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| February 2<br />
| [https://www.i2m.univ-amu.fr/perso/luisa.paoluzzi/hple.html Luisa Paoluzzi] (University of Aix-Marseille)<br />
| tba<br />
| <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| [http://www.math.ubc.ca/~liam/ Liam Watson] (University of British Columbia)<br />
| tba<br />
| <br />
|- style="vertical-align:top;"<br />
| February 16<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-11-12T16:49:12Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
[http://lewark.de/lukas/marengon-slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fa2bba4dafe69.33210586 Video]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/taniguchi_slides.pdf Slides],<br />
[https://mediathek2.uni-regensburg.de/playthis/5fad2a342a1054.47376996 Video]<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
| I'll give a combinatorial and down-to-earth definition of the symmetric gl(1) homology. It is a (non-trivial) link homology which categorifies the trivial link invariant (equal to 1 on every link). Then I'll explain how to use this construction to obtain colored categorification of the Alexander polynomial. (joint with E. Wagner)<br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 22<br />
| tba<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| January 12<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| January 19<br />
| [https://sites.math.rutgers.edu/~feehan/ Paul Feehan] (Rutgers)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| January 26<br />
| [http://people.brandeis.edu/~ruberman/ Danny Ruberman] (Brandeis)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| February 2<br />
| tba<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| February 9<br />
| tba<br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar.]<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list.]<br />
<br />
<center><br />
<img src="https://appsso.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden,]<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-11-04T08:19:35Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies [http://lewark.de/lukas/marengon-slides.pdf Slides]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
| <br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
| Until now, taut foliations on non-fibered hyperbolic 3-manifolds have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| <i>tba</i><br />
|- style="vertical-align:top;"<br />
| January 12<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-11-03T18:39:49Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies [http://lewark.de/lukas/marengon-slides.pdf Slides]<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
| <br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| Taut foliations from left orders in Heegaard genus 2<br />
| Until now, taut foliations on hyperbolic 3-manifolds with $b_1=0$ have generally been constructed using branched surfaces, whether via sutured manifold hierarchies, spanning surfaces of knot exteriors, or Dunfield's one-vertex triangulations with foliar orientations. In this talk, I introduce a novel taut foliation construction that makes no recourse to branched surfaces. Instead, it starts with a transversely-foliated $\mathbb{R}$-bundle over a Heegaard surface, specified by a real line action from a left-invariant order (when existent) on the fundamental group of the 3-manifold. Relating taut foliations to fundamental group real line actions is a decades old question that interested Thurston, Gabai, and Calegari, and has been revived in recent years by the L-space conjecture. This construction works reliably for genus 2 Heegaard diagrams satisfying mild conditions, explaining certain numerical results of Dunfield.<br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| <i>tba</i><br />
|- style="vertical-align:top;"<br />
| January 12<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-10-31T09:14:53Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Talks in fall/winter 2020/21==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:120px;" | November 3<br />
| style="width:300px;" | [https://guests.mpim-bonn.mpg.de/marengon/ Marco Marengon] (MPIM Bonn)<br />
| style="width:400px;" | Non-orientable knot cobordisms and torsion order in Floer homologies<br />
| style="width:600px;" | Given an orientable knot cobordism between classical knots K and K', Juhász, Miller, and Zemke proved an inequality involving the torsion order of the knot Floer homology of K and K' and the Euler characteristic and the number of local maxima appearing in the cobordism. <br />
In our work, we prove analogous inequalities for unorientable knot cobordisms, using unoriented versions of instanton and knot Floer homology. Much of the subtlety in our argument lies in the fact that we need to choose more complicated decorations on the surface than the ones appearing in Juhász-Miller-Zemke's case. <br />
We also introduce unoriented versions of the band unknotting number and of the refined cobordism distance and apply our results to give bounds on these based on the torsion orders of the Floer homologies. As an application, I will exhibit a family of knots all of which bound an embedded Möbius band in B^4, but for which the unorientable refined cobordism distance from the unknot is arbitrarily large. <br />
This is joint work with Sherry Gong.<br />
|- style="vertical-align:top;"<br />
| November 10<br />
| [https://sites.google.com/view/masaki-taniguchis-homepage Masaki Taniguchi] (Riken)<br />
| Filtered instanton Floer homology and the 3-dimensional homology cobordism group<br />
| We introduce a family of real-valued homology cobordism invariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the 1/n-surgeries (n>0) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.<br />
|- style="vertical-align:top;"<br />
| November 17<br />
| [https://lrobert.perso.math.cnrs.fr/ Louis-Hadrien Robert] (Luxembourg)<br />
| Categorification of 1 and of the Alexander polynomial<br />
| <br />
|- style="vertical-align:top;"<br />
| November 24<br />
| [https://www.dpmms.cam.ac.uk/~sr727/ Sarah Rasmussen] (Cambridge)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 1<br />
| [https://www.bc.edu/bc-web/schools/mcas/departments/math/people/faculty-directory/tao-li.html Tao Li] (Boston College)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 8<br />
| [https://web.stanford.edu/~cm5/ Ciprian Manolescu] (Stanford)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
| December 15<br />
| [https://sites.google.com/view/siddhi-krishna/home Siddhi Krishna] (Georgia Tech)<br />
| <i>tba</i><br />
|- style="vertical-align:top;"<br />
| January 12<br />
| [http://math.columbia.edu/~nks/ Nick Salter] (Columbia)<br />
| <i>tba</i><br />
| <br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Past talks in spring 2020==<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-10-06T08:08:43Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar is on summer break, and will resume in November 2020.<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
[[Past talk of the Regensburg low-dimensional geometry and topology seminar | List of past talks in spring/summer 2020, with slides and videos]]<br />
<br />
==Talks in fall/winter 2020/21==<br />
(coming soon!)<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-29T14:49:39Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| Large-scale geometry of big mapping class groups [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/mann-slides.pdf Slides]<br />
| Mapping class groups of infinite type surfaces are not finitely generated (nor even are they locally compact) groups, but in many cases one can still meaningfully talk about their large scale geometry. I will explain joint work with Kasra Rafi on the problem of which surfaces have mapping class groups with nontrivial coarse geometry, and how this relates to questions of actions on arc and curve complexes. <br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| From SL(2) to GL(N) foam evaluation<br />
| Foams in 3-space are cobordisms between planar graphs that are heavily used in link homology theories. In this talk we'll explain how foam theory can be built from the ground up starting with an evaluation of closed foams, for SL(2) foams, then GL(2) foams, and finally GL(N) foams for any N. The talk is based on joint work with Louis-Hadrien Robert and on L.-H. Robert and Emmanuel Wagner's work on foam evaluation.<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| Thinness and Conway spheres<br />
| style="width:700px;"| When does Dehn surgery along a knot give an L-space? More generally, when does splicing two knot complements give an L-space? Hanselman, Rasmussen and Watson gave very compelling answers to these questions using their technology of immersed curves for three-manifolds with torus boundary. Similar invariants have been developed for four-ended tangles. We use those invariants to study various notions of thinness in both Heegaard Floer and Khovanov homology from the perspective of tangle decompositions along Conway spheres. Interestingly, our results bear strong resemblance to the aforementioned results about L-spaces. Also, we observe strong similarities between Heegaard Floer and Khovanov homology that lead us to ask: What is a thin link? This is joint work with Artem Kotelskiy and Liam Watson.<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee9edb47fc906.61309061 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/matic-slides.pdf Slides]<br />
| In this joint work with Cagatay Kutluhan, Jeremy Van Horn-Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union infinity. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| The trace embedding lemma and PL surfaces<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ef24a70b54d45.05325323 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/piccirillo-slides.pdf Slides]<br />
| 4-manifold topologists have long been interested in understanding smooth (resp. topological) embedded surfaces in smooth (resp. topological) 4-manifolds, and as such have developed rich suites of tools for obstructing the existence of smooth (resp. topological) surfaces. Understanding PL surfaces in smooth 4-manifolds has historically garnered less interest, but several problems about PL surfaces have recently arisen in modern lines of questioning. Presently there are far fewer tools available to obstruct PL surfaces. In this talk, I’ll discuss how to use a classical observation, called the trace embedding lemma, to repurpose smooth surface obstructions as PL surface obstructions. I’ll discuss applications of these retooled obstructions to problems about spinelessness, exotica, and geometrically simply connectedness. This is joint work with Kyle Hayden.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-28T18:23:16Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| Large-scale geometry of big mapping class groups<br />
| Mapping class groups of infinite type surfaces are not finitely generated (nor even are they locally compact) groups, but in many cases one can still meaningfully talk about their large scale geometry. I will explain joint work with Kasra Rafi on the problem of which surfaces have mapping class groups with nontrivial coarse geometry, and how this relates to questions of actions on arc and curve complexes. <br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee9edb47fc906.61309061 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/matic-slides.pdf Slides]<br />
| In this joint work with Cagatay Kutluhan, Jeremy Van Horn-Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union infinity. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| The trace embedding lemma and PL surfaces<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ef24a70b54d45.05325323 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/piccirillo-slides.pdf Slides]<br />
| 4-manifold topologists have long been interested in understanding smooth (resp. topological) embedded surfaces in smooth (resp. topological) 4-manifolds, and as such have developed rich suites of tools for obstructing the existence of smooth (resp. topological) surfaces. Understanding PL surfaces in smooth 4-manifolds has historically garnered less interest, but several problems about PL surfaces have recently arisen in modern lines of questioning. Presently there are far fewer tools available to obstruct PL surfaces. In this talk, I’ll discuss how to use a classical observation, called the trace embedding lemma, to repurpose smooth surface obstructions as PL surface obstructions. I’ll discuss applications of these retooled obstructions to problems about spinelessness, exotica, and geometrically simply connectedness. This is joint work with Kyle Hayden.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-22T15:27:01Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| The trace embedding lemma and PL surfaces<br />
| 4-manifold topologists have long been interested in understanding smooth (resp. topological) embedded surfaces in smooth (resp. topological) 4-manifolds, and as such have developed rich suites of tools for obstructing the existence of smooth (resp. topological) surfaces. Understanding PL surfaces in smooth 4-manifolds has historically garnered less interest, but several problems about PL surfaces have recently arisen in modern lines of questioning. Presently there are far fewer tools available to obstruct PL surfaces. In this talk, I’ll discuss how to use a classical observation, called the trace embedding lemma, to repurpose smooth surface obstructions as PL surface obstructions. I’ll discuss applications of these retooled obstructions to problems about spinelessness, exotica, and geometrically simply connectedness. This is joint work with Kyle Hayden.<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| Groups that recognize homeomorphisms<br />
| Given a sufficiently rich group of homeomorphisms of a space, it is sometimes possible to reconstruct the action of a homeomorphism from purely algebraic information from the group. This is an old (if vague!) principle, but in this talk I will discuss a new precise version from joint work with Maxime Wolff, and how we use it to give a new short proof of a recent result of Kim and Koberda on diffeomorphism groups of 1-manifolds: one can distinguish the diffeomorphism groups of different regularities (C<sup>r</sup> versus C<sup>s</sup> versus smooth...) by their finitely generated subgroups. <br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee9edb47fc906.61309061 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/matic-slides.pdf Slides]<br />
| In this joint work with Cagatay Kutluhan, Jeremy Van Horn-Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union infinity. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-22T15:26:30Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| The trace embedding lemma and PL surfaces<br />
| 4-manifold topologists have long been interested in understanding smooth (resp. topological) embedded surfaces in smooth (resp. topological) 4-manifolds, and as such have developed rich suites of tools for obstructing the existence of smooth (resp. topological) surfaces. Understanding PL surfaces in smooth 4-manifolds has historically garnered less interest, but several problems about PL surfaces have recently arisen in modern lines of questioning. Presently there are far fewer tools available to obstruct PL surfaces. In this talk, I’ll discuss how to use a classical observation, called the trace embedding lemma, to repurpose smooth surface obstructions as PL surface obstructions. I’ll discuss applications of these retooled obstructions to problems about spinelessness, exotica, and geometrically simply connectedness. This is joint work with Kyle Hayden.<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| Groups that recognize homeomorphisms<br />
| Given a sufficiently rich group of homeomorphisms of a space, it is sometimes possible to reconstruct the action of a homeomorphism from purely algebraic information from the group. This is an old (if vague!) principle, but in this talk I will discuss a new precise version from joint work with Maxime Wolff, and how we use it to give a new short proof of a recent result of Kim and Koberda on diffeomorphism groups of 1-manifolds: one can distinguish the diffeomorphism groups of different regularities (C<sup>r versus C<sup>s versus smooth...) by their finitely generated subgroups. <br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee9edb47fc906.61309061 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/matic-slides.pdf Slides]<br />
| In this joint work with Cagatay Kutluhan, Jeremy Van Horn-Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union infinity. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T18:03:17Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union infinity. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T18:02:55Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set of positive integers union &infin;. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T18:01:56Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class. {{math|{{mathbb|Z}}<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T18:00:29Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, &infin; for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T17:59:48Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute;th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-06-11T17:59:29Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| Spectral order invariant and obstruction to Stein fillability<br />
| In this joint work with Ca\ugatay Kutluhan, Jeremy Van Horn- Morris and Andy Wand, we define an invariant of contact structures in dimension three arising from introducing a filtration on the boundary operator in Heegaard Floer homology. This invariant takes values in the set $\Z_{\geq0}\cup\{\infty\}$. It is zero for overtwisted contact structures, $\infty$ for Stein fillable contact structures, non-decreasing under Legendrian surgery, and computable from any supporting open book decomposition. I will give the definition and discuss computability of the invariant. As an application, we give an easily computable obstruction to Stein fillability on closed contact 3-manifolds with non-vanishing Ozsv&aacute; th-Szab&oacute; contact class.<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ec4e9c4e69571.49997295 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| [https://mediathek2.uni-regensburg.de/playthis/5eceb8f9a9cf89.80472887 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/li-slides.pdf Slides]<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| Instanton Floer homology for tangles and applications in Khovanov homology<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ee0ca239787b3.80733080 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/zhang-slides.pdf Slides]<br />
|In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-19T12:34:24Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-19T12:33:40Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
|[https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/quasimorphismpres.pdf Slides]<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| [https://sites.google.com/view/lpiccirillo/home Lisa Piccirillo] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
| July 21<br />
| [http://people.maths.ox.ac.uk/lackenby/ Marc Lackenby] (University of Oxford)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| [https://mediathek2.uni-regensburg.de/playthis/5ebcdd40adff68.61547947 Video], [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-13T21:29:32Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Upcoming Talks==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/richard.webb.html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| Instanton Floer homology and the depth of taut foliations<br />
| Sutured manifold hierarchy is a powerful tool introduced by Gabai to study the topology of 3-manifolds. The length of a sutured manifold hierarchy gives us a measurement of how complicated the sutured manifold is. Also, using this tool, Gabai proved the existence of finite depth taut foliations. However, he didn’t discuss how finite the depth could be.<br />
<br />
Sutured Instanton Floer homology was introduced by Kronheimer and Mrowka and is defined on balanced sutured manifolds. In this talk, I will explain how sutured instanton Floer homology could offer us bounds for the minimal length of a sutured hierarchy and the minimal depth of a foliation on a fixed balanced sutured manifold.<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| NN<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | July 14<br />
| style="width:180px;"| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| style="width:350px;"| tba<br />
| style="width:700px;"| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Past Talks (with slides and videos for download)==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Downloads<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces <br />
| style="width:100px;" | [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video]<br />
| style="width:600px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| Video (upcoming), [https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/calegari-slides.pdf Slides]<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-11T19:52:38Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Program==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video of the talk]<br />
| style="width:700px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/en/researchers/richard-webb(efcdb4db-86bd-4297-9a21-ce7ce78e15bf).html Richard Webb] (University of Manchester)<br />
| Quasimorphisms on diffeomorphism groups<br />
| I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| NN<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 7<br />
| [https://www.math.columbia.edu/~khovanov/ Mikhail Khovanov] (Columbia University)<br />
| Introduction to foam evaluation and its uses<br />
| tba<br />
|- style="vertical-align:top;"<br />
| July 14<br />
| [https://cbz20.raspberryip.com/ Claudius Zibrowius] (UBC Vancouver)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-11T07:52:45Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Program==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video of the talk]<br />
| style="width:700px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/en/researchers/richard-webb(efcdb4db-86bd-4297-9a21-ce7ce78e15bf).html Richard Webb] (University of Manchester)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| NN<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminarRegensburg low-dimensional geometry and topology seminar2020-05-11T07:51:54Z<p>Boj44979: </p>
<hr />
<div>__NOTOC__<br />
<br />
=<big>Regensburg low-dimensional geometry and topology seminar</big>=<br />
<br />
The seminar takes place on <b>Zoom</b> (see information below) every <b>Tuesday at 16:00 CET</b> (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).<br />
<br />
Talks are split into a 40 minute and a 20 minute part, with a 15 minute tea break in between (you have to brew your own tea).<br />
<br />
==Program==<br />
{| class="wikitable" style="border: 0px;"<br />
! Date <br />
! Speaker<br />
! Title<br />
! Abstract<br />
|- style="vertical-align:top;"<br />
| style="width:80px;" | May 5<br />
| style="width:180px;" | [http://people.math.harvard.edu/~kronheim/ Peter Kronheimer] (Harvard)<br />
| style="width:350px;" | Genus versus double-points for immersed surfaces [https://mediathek2.uni-regensburg.de/playthis/5eb3e138b98b91.38823016 Video of the talk]<br />
| style="width:700px;" | If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.<br />
|- style="vertical-align:top;"<br />
| May 12<br />
| [http://math.uchicago.edu/~dannyc/ Danny Calegari] (University of Chicago)<br />
| Taut foliations leafwise branch cover the 2-sphere<br />
| A co-oriented foliation of an oriented 3-manifold is taut if and only if there is a map from the 3-manifold to the 2-sphere which is a branched cover when restricted to each leaf. I shall give two proofs of this theorem and explain its relation to theorems of Ghys and Donaldson.<br />
|- style="vertical-align:top;"<br />
| May 19<br />
| [https://www.research.manchester.ac.uk/portal/en/researchers/richard-webb(efcdb4db-86bd-4297-9a21-ce7ce78e15bf).html Richard Webb] (University of Manchester)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| May 26<br />
| [https://sites.google.com/view/zhenkun Zhenkun Li] (MIT)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 2<br />
| <i>no talk (pentecoste)</i><br />
| <br />
| <br />
|- style="vertical-align:top;"<br />
| June 9<br />
| [https://web.math.princeton.edu/~bz/ Boyu Zhang] (Princeton)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 16<br />
| [https://www.math.uga.edu/directory/people/gordana-matic Gordana Matic] (Univ. of Georgia/MPIM Bonn)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 23<br />
| <br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"<br />
| June 30<br />
| [https://e.math.cornell.edu/people/mann/index.html Kathryn Mann] (Cornell)<br />
| tba<br />
| tba<br />
|- style="vertical-align:top;"|}<br />
<br />
The program is also contained in the [https://calendar.google.com/calendar/embed?src=lkphrh6v1m5v694ijk4nsq5iqc%40group.calendar.google.com&ctz=Europe%2FZurich RLGTS Google Calendar].<br />
To receive announcements by email, sign up to our [https://www-mailman.uni-regensburg.de/mailman/listinfo/math.rlgts mailing list].<br />
<br />
<center><br />
<img src="https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/regensburg.jpg" alt="Regensburg" style="width:60%;"></center><br />
<br />
==Zoom information==<br />
Zoom Meeting ID: <b>924 2829 6353</b><br />
<br />
The <b>password</b> is the answer to the following riddle (lower case, singular, no article): <i>As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold). </i><br />
<br />
We encourage you to enable your video, for a more interactive atmosphere. The talks are recorded and made available on this webpage, including audio and video of questions from the audience.<br />
<br />
==Organizers==<br />
[https://sites.google.com/view/jpbowden/ Jonathan Bowden],<br />
[http://lewark.de/lukas/ Lukas Lewark],<br />
[http://www.mathematik.uni-regensburg.de/zentner/ Raphael Zentner].</div>Boj44979