4:00–5:00 pm
Ryerson Physical Laboratory, Room 251
1100 East 58th Street
Chicago, IL 60637
Given a Lie group \(G\) acting on a manifold \(M\) we can ask: how does \(L^2(M)\) decompose as a representation of \(G\)? For example, when \(G\) is the group of rotations acting on a sphere, spherical harmonics give an explicit answer to this. I will explain how (refined versions of) this question are related to the theory of periods of automorphic forms. (I will explain what is meant by the theory of periods, but some familiarity with automorphic forms will be needed for this part of the talk.) Then I will discuss a duality that switches the question with a similar question for the dual group. The duality is conjectural but there is a lot of experimental evidence for it. Joint work, in progress, with David Ben-Zvi and Yiannis Sakellaridis.