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| May 18
 
| May 18
 
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)
 
| [https://math.virginia.edu/people/ra5aq/ Rostislav Akhmechet] (Virginia)
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| Anchored foams and annular homology
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| 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.
 
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| May 25
 
| May 25

Revision as of 15:30, 6 May 2021


Regensburg low-dimensional geometry and topology seminar

The seminar takes place on Zoom (see information below) every Tuesday at 16:00 CET (that is 7am on the US west coast, 10am on the US east coast, 10pm in China and 11pm in Korea and Japan).

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...).

Talks in spring/summer 2021

The program is also contained in the RLGTS Google Calendar. To receive announcements by email, sign up to our mailing list.

Date Speaker Title Abstract
April 27 Guillem Cazassus (Oxford) The earring correspondence of the pillowcase

Slides Video

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.

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.

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 Herald, Paul Kirk and Artem Kotelskiy.

May 4 Zoltán Szabó (Princeton) Knot Floer homology constructions and the Pong Algebra

Slides Video

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
May 11 John Baldwin (Boston College) Instanton L-spaces and splicing 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.
May 18 Rostislav Akhmechet (Virginia) Anchored foams and annular homology 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.
May 25
June 1 Arunima Ray (MPIM Bonn)
June 8 Cameron Gordon (UT Austin)
June 15 Thomas Barthelmé (Queen's University)
June 22
June 29 Alexandra Kjuchukova (Notre Dame)
July 6
July 13 Steven Frankel (Washington University in St. Louis)
Regensburg

Past talks

List of past talks in spring/summer 2020 and fall/winter 2020/21, with slides and videos

Zoom information

Zoom Meeting ID: 924 2829 6353

The password is the answer to the following riddle (lower case, singular, no article): As a topologist, what do you typically glue together from charts? (Hint: It's not an orbifold).

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.

Organizers

Jonathan Bowden, Lukas Lewark, Raphael Zentner.