Representation Theory and Moduli Spaces

Brown University, Providence RI

Investigators

Abstract

This research lies in the intersection of several fields of mathematics, including representation theory, algebraic geometry, number theory, and mathematical physics. In particular, new connections between the Langlands program (which originates in number theory - arguably the oldest subject in mathematics) and quantum field theory will be explored. On the more technical side the PI will study various moduli spaces attached to affine Kac-Moody groups (such as the affine Grassmannian, Uhlenbeck compactifications of moduli spaces of principal bundles on some algebraic surfaces, and some others) in order to attack the following problems: 1) a construction of local L-functions for representations of p-adic groups, 2) Hecke algebras and Eisenstein series for affine Kac-Moody groups over functional fields, and 3) instanton counting and other problems in 4-dimensional gauge theory.