Geometry and Topology Seminar 2019-2020
The seminar will be held in room B901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm
|September 10||Yong-Geun Oh (UW Madison)||local|
|September 17||Leva Buhovsky (U of Chicago)||Yong-Geun|
|September 24||Leonid Polterovich (Tel Aviv U and U of Chicago)||Yong-Geun|
|October 8||Sean Paul (UW Madison)||local|
|October 15||Conan Leung (Chinese U. of Hong Kong)||Honorary fellow, local|
|October 22||Markus Banagl (U. Heidelberg)||Maxim|
|October 29||Ke Zhu (U of Minnesota)||Yong-Geun|
|November 5||Sergei Tabachnikov (Penn State)||Gloria|
|January 21||Mohammed Abouzaid (Clay Institute & MIT)||Yong-Geun|
Yong-Geun Oh (UW Madison)
Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants
Gopakumar-Vafa BPS invariant is some integer counting invariant of the cohomology of D-brane moduli spaces in string theory. In relation to the Gromov-Witten theory, it is expected that the invariant would coincide with the `number' of embedded (pseudo)holomorphic curves (Gopakumar-Vafa conjecture). In this talk, we will explain the speaker's recent result that the latter integer invariants can be defined for a generic choice of compatible almost complex structures. We will also discuss the corresponding wall-crossing phenomena and some open questions towards a complete solution to the Gopakumar-Vafa conjecture.
Leva Buhovsky (U of Chicago)
On the uniqueness of Hofer's geometry
In this talk we address the question whether Hofer's metric is unique among the Finsler-type bi-invariant metrics on the group of Hamiltonian diffeomorphisms. The talk is based on a recent joint work with Yaron Ostrover.
Leonid Polterovich (Tel Aviv U and U of Chicago)
Poisson brackets and symplectic invariants
We discuss new invariants associated to collections of closed subsets of a symplectic manifold. These invariants are defined through an elementary variational problem involving Poisson brackets. The proof of non-triviality of these invariants requires methods of modern symplectic topology (Floer theory). We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics. The talk is based on a work in progress with Lev Buhovsky and Michael Entov.
Sean Paul (UW Madison)
Canonical Kahler metrics and the stability of projective varieties"
I will give a survey of my own work on this problem, the basic reference is: http://arxiv.org/pdf/0811.2548v3
Conan Leung (Chinese U. of Hong Kong)
Markus Banagl (U. Heidelberg)
Ke Zhu (U of Minnesota)
Sergei Tabachnikov (Penn State)
Mohammed Abouzaid (Clay Institute & MIT)