Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations.

I will talk about some applications of the theory of Higgs bundles to basic questions on the topology of the moduli space of (mainly symplectic) local systems on a Riemann surface. I will try to motivate the notion of polystability, which is a crucial ingredient in the relation between Higgs bundles and local systems, and explain the role played by Hitchin's functional as a Morse function.