Mirror symmetry for Higgs bundles

Algebraic Geometry and Topology Seminar

I will first introduce the moduli spaces of Higgs bundles that appear in the Hausel-Thaddeus topological mirror symmetry conjecture, present the context, the different proofs and possible generalisations. In particular I will explain the p-adic integration approach of Groechenig, Wyss and Ziegler. Finally, I will present my result, which is a generalisation beyond the coprime case of the key intermediate step of this approach, which we call a non-archimedean topological mirror symmetry.