Philip Boalch - Nonabelian Hodge spaces and nonlinear representation theory
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2017-06-12

Abstract:
The theory of connections on curves and Hitchin systems is something like a “global theory of Lie groups”, where one works over a Riemann surface rather than just at a point.  We’ll describe how one can take this analogy a few steps further by attempting to make precise the class of rich geometric objects that appear in this story (including the non-compact case), and discuss their classification, outlining a theory of “Dynkin diagrams” as a step towards classifying some examples of such objects.