Overview of Restricted Geometric Langlands Theory

Explore a detailed seminar talk that delves into the categorical version of the global unramified geometric Langlands conjecture, focusing on its formulation with coefficients in various sheaf theories. Learn about the groundbreaking work by Arinkin-Gaitsgory-Kazhdan-Raskin-Rozenblyum-Varshavsky and their concept of moduli stack of local systems with "restricted variation." Understand how this formulation, while potentially weaker in de Rham and Betti settings, encompasses significant aspects of the theory including Hecke eigensheaves. Discover how this represents the first categorical equivalence formulation for l-adic coefficients, and examine its arithmetic implications when working with curves over finite fields through the categorical trace of Frobenius. Gain insights into how this approach provides unconditional refinements to V. Lafforgue's established unramified spectral decomposition of automorphic forms.