

Arithmetic geometry seminar
September 26, 2016 17:00–19:00, Independent University of Moscow






Fundamental Lemma
V. Vologodsky^{} ^{} Department of Mathematics, National Research University "Higher School of Economics"

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Abstract:
The Fundamental Lemma is a combinatorial statement on the orbital integrals for reductive group over padic fields. It was formulated as a conjecture by Langlands in 1983 and proven by Ngo in 2009 (Ngo was awarded Fields Medal for his proof). In my talk I will explain the statement of the Lemma, its relation to the Langlands program and prove the Lemma for $SL(2)$. Next time, Vasya Krylov will explain Ngo's strategy in general (in particular, he will talk about the Hitchin fibration).
We mostly follow Nadler's expostion, see his
survey.

