Shtukas and Global Langlands for Function Fields - Talk 37

Explore a detailed seminar talk where Aaron Slipper presents V. Lafforgue's groundbreaking proof of global Langlands for arbitrary reductive groups G, focusing on the "Galois to automorphic" direction. Begin with a comprehensive review of global Langlands and understand why Hecke compatibility alone cannot fully constrain the Langlands correspondence. Delve into geometric Satake before examining the stack of shtukas and their intersection cohomology sheaves' remarkable properties within the coweight stratification. Learn how excursion operators expand the Hecke algebra to uniquely determine the Langlands decomposition. Conclude with insights into Drinfeld's reinterpretation of Lafforgue's work, which laid the foundation for subsequent AGKRRV developments. The March 27, 2024 presentation spans advanced mathematical concepts across function fields and representation theory.