Lev Borisov

Recent developments in the vertex algebra approach to toric mirror symmetry



Abstract

Vertex algebra approach to mirror symmetry aims to describe mirror symmetry at the level of N=2 vertex (chiral) algebras which arise from the half-twisted sigma models. I will describe the known results in this direction, as well as recent developments. Specifically, I will talk about the applications of vertex algebra approach to the unification of Berglund-Hubsch and Batyrev's versions of mirror symmetry. I will also describe the application of the vertex algebra approach to (0,2) sigma models on the quintic.