Number Theory Seminar
Wednesday, March 27, 2024, 3:15pm, Physics 119
Matthew Sunohara (University of Toronto, Mathematics)
Stable Paley-Wiener theorems and stable transfer operators

Abstract:

Given two real or p-adic quasi-split groups and a bounded L-embedding between their L-groups, the local Langlands correspondence yields a functorial transfer map between their sets of stable tempered characters. Langlands asked whether the functorial transfer map can be interpolated by a continuous linear operator between spaces of stable distributions, or equivalently, whether its transpose exists, a so-called stable transfer operator between spaces of stable orbital integrals. Stable transfer operators can be used in comparisons of trace formulae and their study is the local part of Beyond Endoscopy, the strategy proposed by Langlands for proving the principle of functoriality. We will discuss Paley-Wiener theorems for various spaces of stable orbital integrals, their application in establishing the existence and some properties of stable transfer operators, and some explicit examples of stable transfer operators.

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