## Topology Seminar (Main Talk): Distinguishing fillings using dynamics of Fukaya categories

Seminar | October 3 | 4-5 p.m. | 3 Evans Hall

Yusuf Baris Kartal, MIT

Department of Mathematics

One can construct the open symplectic mapping torus $T_\phi$ for a given a Weinstein manifold $M$ and a compactly supported symplectomorphism $\phi$. Its contact boundary is independent of $\phi$ and is equal to contact boundary of $T_0\times M$ where $T_0$ is the torus with a small ball removed. In this talk, we will outline a method to distinguish the fillings $T_\phi$ and $T_0\times M$. We will exploit the dynamics and deformation theory of the (wrapped) Fukaya categories, where the dynamics of the same sort is invisible at a geometric level.

c_abbott@berkeley.edu