CMSA/Tsinghua Math-Science Literature Lecture: Peng Shan. Bridging affine vertex algebras and affine Springer fibres

 In this talk, I would like to explain a program which aims to build relationships between affine Springer theory and representations of simple affine vertex algebras. We will discuss some explicit correspondences for admissible levels, and formulate some new conjectures about representations of simple affine vertex algebras at nonadmissible levels and their associated varieties. This is based on joint work with Dan Xie, Wenbin Yan and Qixian Zhao.