Hebrew University topology and geometry seminar

Abstract: 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, representations of G naturally appear as spaces of sections of line bundles, and by mirror symmetry they should also be realized in Lagrangian Floer cohomology groups.
This talk is based on joint work with Yanki Lekili and Nick Sheridan.