Speaker:  Daniil Klyuev (MIT)

Title:  Analytic Langlands correspondence for G = P GL(2, ℂ)

Abstract:  Analytic Langlands correspondence was proposed by Etingof, Frenkel and Kazhdan based on ideas and results of Langlands, Teschner, Braverman-Kazhdan and Kontsevich. Let X be a smooth irreducible projective curve over ℂ, G be a semisimple group. On one side of this conjectural correspondence there are G^V-opers on X satisfying a certain condition ({\it real} opers), where G^V is Langlands dual group. On the other side there are certain operators on L2(Bun_G), called Hecke operators, where Bun_G is the variety associated to the moduli stack of stable G-bundles on X and L2(Bun_G) is a Hilbert space of square-integrable half-densities. I will describe the main picture and present new results in this direction. Partially based on joint projects with A. Wang and S. Raman.