Manish Patnaik : Central Extensions of Loop Groups and local Riemann-Roch formulas

Posted by , part of the Algebraic Geometry Seminar.

At

March 4, 2010, 4 p.m.

In

SEO 636

Abstract

The local Riemann-Roch problem on certain simple surfaces may be reformulated in terms of the problem of comparing various central extensions of loop groups. Using an adelic version of this construction (over function fields of positive characteristic), we can interpret the points of certain arithmetic quotients of loop groups as bundles on a surface together with some information about the second Chern class of the bundle. We will sketch the connection with Eisenstein series on loop groups. This is joint work with Howard Garland.