Seminar on Symplectic Topology, December 28, 2023.

• 23. December, 2023
• Comments (0)

The meeting of the Seminar on Symplectic Topology will be held on Thursday, December 28, 2023, in room 840 of the Faculty of Mathematics, starting at 2 p.m.
 
Lecturer: Filip Živanović, Simons Center for Geometry and Physics, Stony Brook

Lecture title: FILTRATIONS ON COHOMOLOGY INDUCED BY FLOER THEORY

Abstract: In this talk, I will talk about symplectic manifolds that admit pseudo-holomorphic C*-actions, and that are proper above a convex base. Examples of these spaces include symplectic quotients of R^2n, such as toric manifolds, and many resolutions of singularities. I will explain how Floer theory with data obtained from these C*-actions induces filtration on (quantum) cohomology of these manifolds, given as a type of spectral invariant. The fact that they come from C*-action makes them somewhat computable in practice, which I will show through the examples. Time permitting, we will compare this filtration with other known filtrations on the cohomologies of these spaces. This talk is based on joint work with Alexander Ritter.