Geometry and Topology Seminar 2019-2020: Difference between revisions
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===Leonid Polterovich (Tel Aviv U and U of Chicago)=== | ===Leonid Polterovich (Tel Aviv U and U of Chicago)=== | ||
''Poisson brackets and symplectic invariants'' | ''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)=== | ===Sean Paul (UW Madison)=== | ||
Revision as of 13:59, 22 September 2010
Fall 2010
The seminar will be held in room B901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm
| date | speaker | title | host(s) |
|---|---|---|---|
| September 10 | Yong-Geun Oh (UW Madison) |
Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants |
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) |
Canonical Kahler metrics and the stability of projective varieties |
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 |
Abstracts
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)
TBA
Markus Banagl (U. Heidelberg)
TBA
Ke Zhu (U of Minnesota)
TBA
Sergei Tabachnikov (Penn State)
TBA