Number Theory Seminar

The fundamental lemma is an identity of integrals central to the Langlands programme which was proved by Ngô in 2008. His proof infers the fundamental lemma from a statement about the cohomology of moduli spaces of Higgs bundles, called geometric stabilisation. In this talk I'll discuss a new perspective on geometric stabilisation, provided by p-adic integration. We will see that there exists a close philosophical link between mirror symmetry for moduli spaces of Higgs bundles (à la Hausel-Thaddeus) and the fundamental lemma. This is joint work with Wyss and Ziegler.