Given a representation of the fundamental group of a Riemann surface, the geometric Langlands correspondence gives a perverse sheaf on the moduli space Bun of vector bundles, hence a representation of the fundamental group of a Zariski open subset of Bun. Ron Donagi and Tony Pantev made conjectures and initiated a program of analyzing this relationship using the nonabelian Hodge correspondence between Higgs bundles and representations of fundamental groups. The picture they developed was also related to what Kapustin and Witten called "electro-magnetic duality". After a brief review of the nonabelian Hodge correspondence, we'll explain the Donagi-Pantev picture and then discuss our current work on this project.

### Penn Mathematics Colloquium

Wednesday, April 12, 2023 - 3:45pm

#### Carlos Simpson

Université Côte d'Azur, Nice and Penn