Cable Car Algebra Seminar: Automorphic Frobenius reciprocity and the Orbit Method

Cable Car Algebra Seminar: Automorphic Frobenius reciprocity and the Orbit Method

Cable Car Algebra Seminar: Automorphic Frobenius reciprocity and the Orbit Method

Thursday, June 5, 2025
  • Lecturer: Andre Reznikov (BIU)
  • Organizer: Max Gurevich, Anton Khoroshkin, Danny Neftin, Howard Nuer, Ofir Gorodetsky
  • Location: Technion, Amado Building, Room 814
Abstract:
Automorphic functions and representations are central for Number Theory. Automorphic Frobenius functional amounts to evaluation of automorphic functions the identity. From a point of view of Functional Analysis it is natural to determine a norm of Automorphic Frobenius functional as a functional on an (infinite dimensional) irreducible unitary automorphic representation. Such bounds provide bounds on values of automorphic functions, and sometimes could be translated into bounds on important number-theoretic quantities (e.g., on L-functions). I discuss recent approach of P. Nelson and A. Venkatesh (Acta Math. 226 (2021), no. 1, 1-209) which is based on a "geometrization" of this question via their quantitative version of the Orbit Method of A. Kirillov. This led them to a discovery of a "hidden symmetry" and an unexpected employment of Ratner's theorem. For simplicity, my discussion will be restricted to the group SL(2,R) while the general case is discussed in arXiv:2408.10793.
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