Hecke Operators for Algebraic Curves Over Local Non-Archimedian Fields - A Survey of Recent Results

Explore a detailed mathematical lecture examining Hecke operators and their eigen-functions in the context of G-bundles on smooth projective algebraic curves over local non-archimedian fields. Delve into fundamental definitions of Hecke operators and their action spaces, drawing connections to classical theories involving curves over finite fields. Focus on specific examples of genus zero curves with bundle trivializations at two points, investigating their relationships to p-adic group representation theory and Cherednik algebra representation theory. Learn from collaborative research conducted with P. Etingof, D. Kazhdan, and A. Polishchuk, presented by Sasha Braverman from Toronto/Perimeter as part of the Arithmetic Quantum Field Theory Conference.