Adelic uniformization of moduli of G-bundles
Xinwen Zhu, Harvard

It is well-known from Weil that the isomorphism classes of rank n vector bundles on an algebraic curve can be written as the set of certain double cosets of GL(n,A), where A is the adeles of the curve. Recently, such double coset presentation can be put in the framework of algebraic geometry. I will introduce such adelic uniformization and discuss some of its applications.