# Equivariant structures in mirror symmetry

 Princeton/IAS Symplectic Geometry Seminar Topic: Equivariant structures in mirror symmetry Speaker: James Pascaleff Affiliation: University of Illinois at Urbana-Champaign Date: Friday, October 17 Time/Room: 1:30pm - 2:30pm/S-101 Video Link: http://video.ias.edu/pisgs/2014/1017-JamesPascaleff

When a variety $X$ is equipped with the action of an algebraic group $G$, it is natural to study the $G$-equivariant vector bundles or coherent sheaves on $X$. When $X$ furthermore has a mirror partner $Y$, one can ask for the corresponding notion of equivariance in the symplectic geometry of $Y$. The infinitesimal notion (equivariance for a single vector field) was introduced by Seidel and Solomon (GAFA 22 no. 2), and it involves identifying a vector field with a particular element in symplectic cohomology. I will describe the analogous situation for a Lie algebra of vector fields, and discuss the application of this theory to mirror symmetry of flag varieties. In this situation, we expect to find a close connection to the canonical bases of Gross-Hacking-Keel. This talk is based on joint work with Yanki Lekili and Nick Sheridan.