Notes on the fundamental lemma

The Fundamental Lemma is a conjecture about identities of p-adic integrals that appear in the trace formula for a reductive group.  The conjecture was made by Langlands and Shelstad in the 1980s and was solved in 2008 by Ngo Bao Chau.  For this result, he was awarded a Fields Medal.  This talk will describe some of the general context and history of the fundamental lemma, including the work of Forey, Loeser, and Wyss, who proved a motivic version of the fundamental lemma in August 2023.