Dimitri Wyss - Non-archimedean integrals on the Hitchin fibration
Non-archimedean or p-adic integration is an analytic tool to study rational points of algebraic varieties over finite fields. Dener-Loser and Batyrev have realized that this can be used in some cases to study the topology of complex algebraic varieties. We apply this idea to the moduli spaces of G-Higgs bundles M(G) and show in particular, that for a pair of Langlands dual groups the corresponding moduli spaces have the same non-archimedean volume. As a geometric application we find an agreement of (stringy) Hodge numbers of M(SLn) and M(PGLn) as predicted by a conjecture of Hausel-Thaddeus. For general G this leads to a new proof of the geometric stabilization theorem, a key ingredient in Ngô's proof of the fundamental lemma. This is joint work with Michael Groechenig and Paul Ziegler.