From Geometric to Classical Langlands

Explore the profound connections between geometric and classical Langlands theory in this mathematical lecture delivered by Dennis Gaitsgory from the Max Planck Institute for Mathematics. Delve into the recently established geometric Langlands equivalence and discover how it provides an explicit description of the space of unramified automorphic functions through Langlands parameters. Learn about the derivation of these descriptions and examine their potential applications in proving fundamental properties of automorphic functions, including the Ramanujan and Arthur multiplicity conjectures. Gain insights into cutting-edge research conducted in collaboration with Vincent Lafforgue and Sam Raskin that bridges geometric and classical approaches to one of mathematics' most significant theoretical frameworks. This presentation forms part of the Math Science Lectures in Honor of Raoul Bott series, offering advanced mathematical content suitable for researchers and graduate students working in algebraic geometry, number theory, and representation theory.