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)
Using homotopy theoretic methods, we shall associate to certain classes of singular spaces generalized geometric Poincaré complexes called intersection spaces. Their cohomology is generally not isomorphic to intersection cohomology. In this talk, we shall concentrate on the applications of the new cohomology theory to the equivariant real cohomology of isometric actions of torsionfree discrete groups, to type II string theory and D-branes, and to the relation of the new theory to classical intersection cohomology under mirror symmetry.
Ke Zhu (U of Minnesota)
Sergei Tabachnikov (Penn State)
Mohammed Abouzaid (Clay Institute & MIT)