Perverse Sheaves and Representations of p-adic Groups

Explore the intersection of algebraic geometry and representation theory in this mathematical lecture that examines how perverse sheaves relate to representations of p-adic groups. Learn about Lusztig's groundbreaking 1980s approach that replaced analytic limits with algebro-geometric intermediate extensions when studying representations of matrix groups over finite fields. Discover how continuous functions are determined by their values on dense open subsets and understand how this principle applies to recognizing representations of Lie groups from regular semisimple elements. Examine a recent construction developed with R. Bezrukavnikov that creates perverse sheaves giving rise to positive-depth supercuspidal representations of p-adic groups, including how this work resolves a conjecture of Lusztig in the simplest nontrivial case.