3d mirror symmetry and vertex functions

Abstract: The phenomenon of 3d mirror symmetry is a type of duality for symplectic varieties that is intertwined with some deep objects in algebraic geometry, representation theory, and combinatorics. The main objects of study are certain generating functions arising from quasimap counts that solve q-difference equations described using representation theory. Quasimap counts for a pair of 3d mirror dual varieties are expected to satisfy the same collection of q-difference equations. There are known ways to construct some explicit pairs of 3d mirror dual varieties. However, calculating quasimap counts and comparing the results are nontrivial tasks. I will survey some of the expectations of 3d mirror symmetry, discuss what is presently known, and provide some explicit examples.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar