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).
|May 5||Peter Kronheimer (Harvard)||Genus versus double-points for immersed surfaces Video of the talk||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.|
|May 12||Danny Calegari (University of Chicago)||Taut foliations leafwise branch cover the 2-sphere||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.|
|May 19||Richard Webb (University of Manchester)||Quasimorphisms on diffeomorphism groups||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.|
|May 26||Zhenkun Li (MIT)||tba||tba|
|June 2||no talk (pentecoste)|
|June 9||Boyu Zhang (Princeton)||tba||tba|
|June 16||Gordana Matic (Univ. of Georgia/MPIM Bonn)||tba||tba|
|June 30||Kathryn Mann (Cornell)||tba||tba|
|July 7||Mikhail Khovanov (Columbia University)||Introduction to foam evaluation and its uses||tba|
|July 14||Claudius Zibrowius (UBC Vancouver)||tba||tba|
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.