EVENT DETAILS AND ABSTRACT

Title: Mirror symmetry for Higgs bundles and the fundamental lemma
Speaker: Michael Gröchenig
Speaker Info: Freie Universität Berlin
Brief Description: Note: talk starts at 4pm not 4.10pm!
Special Note:
Abstract:

The fundamental lemma is an integral identity central to the Langlands programme (conjectured to hold in 1979). Despite its ostensibly combinatorial nature it resisted all direct efforts to verify it, until Ngô finally proved it in 2008. One of the unexpected features of Ngô’s argument, was the important role played by the moduli space of Higgs bundles. In this overview talk I will try to convey why this space is capable of hiding such deep arithmetic secrets. Our perspective is different however, as we approach the question from the point of view of mirror symmetry. We will see that there exists a close philosophical link between mirror symmetry for moduli spaces of Higgs bundles (conjectured by Hausel—Thaddeus) and the fundamental lemma. This is joint work with Wyss and Ziegler.