Globalization of Supercuspidal Representations Over Function Fields and Applications - Lecture 3

Explore a graduate-level mathematics lecture focusing on the globalization of supercuspidal representations over function fields, delivered by Professor Wee Teck Gan from the National University of Singapore as Distinguished Visiting Project Professor at Kyoto University. Learn how Poincare series can be utilized to construct cuspidal automorphic representations of connected reductive groups over global function fields with specified supercuspidal local components and prescribed behaviors. Discover the applications of this globalization result in completing the Langlands-Shahidi theory over function fields, including Luis Lomeli's recent findings. Examine how this work combines with Vincent Lafforgue's construction of global Langlands correspondence to prove stability of Langland-Shahidi gamma factors and establish local Langlands correspondence for classical groups. Delve into advanced mathematical concepts including Stokes equations, reversibility principles, fundamental singularities of Stokes flows, the Lorentz reciprocal theorem, Goursat representation of biharmonic fields, conformal mapping, and various boundary value problems.