A cornerstone of the Langlands program, the Fundamental Lemma was a conjecture which has long resisted the efforts of mathematicians until its full proof by Ngô. It is an identity relating $p$-adic orbital integrals on two different reductive groups over the same local field. In this lecture I will present a motivic version of this result, which was obtained with Arthur Forey and Dimitri Wyss. We follow the strategy from a recent new proof of the Fundamental Lemma by Groechenig, Wyss and Ziegler using $p$-adic integration instead of perverse sheaves.
Vladimir Rubtsov, Ilia Gaiur
