Bridging affine vertex algebras and affine Springer fibres

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 correspondence for admissible levels, and formulate some new conjectures about representations of simple affine vertex algebras at integer nonadmissible levels and their associated varieties. This is based on joint work with Dan Xie, Wenbin Yan and Qixian Zhao.