Geometric Sen Theory, Locally Analytic Representations and the Completed Cohomology of Shimura Varieties - Lecture 1

Explore the cutting-edge methods introduced by Lue Pan and further developed by Rodriguez Camargo, Benchao Su, and Tian Qiu in this introductory lecture on geometric Sen theory and locally analytic representations. Delve into the detailed analysis of locally analytic vectors within the completed cohomology of Shimura varieties, a fundamental topic in modern arithmetic geometry and representation theory. Learn how these sophisticated mathematical techniques provide new insights into the structure and properties of cohomological objects associated with Shimura varieties. Gain understanding of the theoretical foundations that connect geometric Sen theory with locally analytic representation theory, examining how these connections illuminate the behavior of cohomological systems in arithmetic contexts. Discover the mathematical framework that underlies recent advances in the field, with particular attention to the methods that have emerged from Pan's pioneering work and subsequent developments by leading researchers in the area.