Equivariant vector bundles on some spherical varieties

Abstract: Spherical varieties are a class of varieties with  group action that simultaneously generalize toric varieties and flag varieties. In this talk, I will explain a generalization of some results of A. Klyachko and S. Kato, which provide "concrete" descriptions of categories of equivariant vector bundles on spherical varieties (via "linear algebraic" data), and discuss some potential applications. This is based on joint work with James Parson.