Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams

Abstract

The theory of 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.

21 pages, to appear in Hitchin's 70th birthday proceedings. v3: more on parahoric bundles, v4: minor improvements/clarifications