Back to Departmental Colloquium: Fall 2025
Departmental Colloquium
Date: Thursday, Nov 6, 2025
Time: 4:00PM - 5:00PM
Location: JWB 335
Aaron Pollack
University of California, San Diego
Title |
The arithmetic of certain automorphic forms |
Abstract |
Suppose G is a non-compact semisimple Lie group, and let G (ℤ) in G be an appropriate infinite discrete subgroup. An automorphic form on G is a complex valued smooth function on G that is left invariant by G (ℤ) and satisfies some particular linear differential equation. They are key players in the Langlands program, and conjecturally encode incredible arithmetic information in a precise way. A simpler (imprecise) conjecture is that automorphic forms, even though defined in an analytic way, can be understood as algebraic objects. I will give some historical background on this problem, and explain some new work. |
Number Theory