Logic Seminar
Francois Loeser
Ecole Normale Superieure
Model Theory and the Fundamental Lemma
Abstract: The Fundamental Lemma is a complicated combinatorial identity between integrals over local fields which plays a central feature in
the Langlands program in the theory of automorphic representations. A proof of the Fundamental Lemma was recently completed by Ngo Bau Chau for which he was awarded a Fields Medal in Hyderabad. His proof, which is geometric in nature, works for functions fields over finite fields. It has been proved previously by Waldspurger, using specific representation theory techniques, that the Fundamental Lemma over p-adic fields - which is the case more relevant for applications to number theory - would follow from the function field case, for p large enough. The aim of our talk is to explain how Waldspurger's result - and similar statements for various versions analogues of the Fundamental Lemma which are not covered by Waldspurger's result - follows at once from a general transfer result allowing to transfer identities between integrals depending on parameters from
functions fields over finite fields to p-adic fields, for large p, which we obtained in collaboration with Raf Cluckers using our theory of motivic integration in a definable setting. To achieve this, one has to carefully encode all the data appearing in the Fundamental Lemma in a definable way. This is joint work with Raf Cluckers and Tom Hales.
This talk is part of Midwest Model Theory Day.
Tuesday October 26, 2010 at 2:30 PM in SEO 636