9/29/2006

Jeff Streets
Duke University

A Geometric Evolution Equation on Principal Bundles

In this talk I will motivate and define a natural geometric  evolution equation on principal bundles.  This flow is a non-trivial  coupling of the usual Ricci flow for a metric and the Yang-Mills flow  for a connection.  I will describe various basic analytic aspects of  this flow, and show a stability-type convergence result on four- manifolds, the targets of primary interest.  Also I will present some  plausible (and powerful) conjectures about the long-time behaviour of  this flow.  If there is time I will describe a related flow coupling  the usual Ricci flow for a metric and a Yang-Mills type flow for  gerbes (local 2-form field strength potentials).