Nonabelian Hodge theory and uniformization

Jun Ho (Peter) Whang , Princeton University
Fine Hall 314

Classical Hodge theory provides a link between the topology and the analytic geometry of a compact Kaehler manifold X via harmonic forms. Similarly, in nonabelian Hodge theory (developed by Simpson based on works of Hitchin, Corlette, Donaldson, Uhlenbeck-Yau, and others), harmonic metrics on vector bundles are used to study the fundamental group of X, a nonabelian topological invariant. In this talk, we give an introduction to these topics. As an application, we sketch a proof of the old uniformization theorem for Riemann surfaces from a Hodge-theoretic point of view.