Geometric Aspects of the p-adic Locally Analytic Langlands Program

Explore the geometric aspects of the p-adic locally analytic Langlands program in this advanced mathematical lecture delivered by Arthur-César Le Bras from Université de Strasbourg. Delve into the geometrization of the p-adic Langlands program, specifically focusing on locally analytic representations on topological Q_p-vector spaces. Learn how to realize locally analytic representations as sheaves on a variant of Fargues-Scholze's stack of G-bundles on the Fargues-Fontaine curve, drawing from joint research with Anschütz, Rodriguez Camargo, and Scholze. Discover the "automorphic" side of this mathematical framework while gaining insights into cutting-edge developments in algebraic number theory and representation theory. This lecture forms part of a comprehensive series that examines both Galois and automorphic perspectives on the p-adic Langlands correspondence, providing essential knowledge for researchers and advanced students working in arithmetic geometry and related fields.