Geometric Aspects of the p-adic Locally Analytic Langlands Correspondence III

Explore advanced geometric aspects of the $p$-adic locally analytic Langlands correspondence in this third lecture by Eugen Hellmann from Universität Münster. Delve into the geometrization of the $p$-adic Langlands program, specifically focusing on locally analytic representations on topological $\mathbb{Q}_p$-vector spaces. Examine the "Galois" side of the correspondence through an introduction to moduli stacks of variants of $p$-adic Galois representations and investigate their geometric properties. Learn about joint research with Hernandez, Schraen, and Heuer that advances understanding of these mathematical structures. Gain insights into how this work complements the "automorphic" side research by Le Bras and collaborators, which realizes locally analytic representations as sheaves on variants of the Fargues-Scholze stack of $G$-bundles on the Fargues-Fontaine curve. This lecture forms part of a comprehensive series examining the geometric foundations underlying modern developments in the $p$-adic Langlands program.