Exponential Volumes in Geometry and Representation Theory
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore a lecture on exponential volumes in geometry and representation theory delivered by Alexander Goncharov from Yale University. Delve into the study of moduli spaces parametrizing hyperbolic structures on topological surfaces with holes and geodesic boundaries. Examine Maryam Mirzakhani's remarkable recursion formulas for volumes and their connections to various areas of mathematics. Investigate a variant of moduli spaces for surfaces with polygonal boundaries and discover how they carry canonical exponential volume forms. Learn about the generalization of these moduli spaces for split simple real Lie groups and their applications in defining a commutative algebra of positive Whittaker functions. Analyze the tropical limits of exponential volumes and their connections to Kontsevich's work on Witten's conjecture. Gain insights into the relationship between tropical limits of positive Whittaker functions and spherical functions for complex Lie groups.
Syllabus
Alexander Goncharov - Exponential Volumes in Geometry and Representation Theory
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
One-Dimensional Objects - Algebraic TopologyInsights into Mathematics via YouTube Distinguishing Monotone Lagrangians via Holomorphic Annuli - Ailsa Keating
Institute for Advanced Study via YouTube Pseudoholomorphic Curves with Boundary - Can You Count Them? Can You Really? - Sara Tukachinsky
Institute for Advanced Study via YouTube Mixing Surfaces, Algebra, and Geometry
Joint Mathematics Meetings via YouTube Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji
International Centre for Theoretical Sciences via YouTube