João Nunes

TITLE: Analytic and Geometric Aspects of Theta Functions

ABSTRACT: We will describe some analytic properties of theta functions on moduli spaces of bundles over curves. In particular, we will relate them to coherent state transforms and heat equations for  compact Lie groups. For classic theta functions and for non-abelian ones at genus 1,  at least, this provides a unitary map between spaces of theta  functions associated to different complex structures on the curve.  Possible applications to more general cases will be mentioned.