Leonidas Alaoglu Memorial Lecture in Mathematics

I will talk about joint work, in progress, with Paul Nelson, where we study microlocal analysis on representations of a Lie group. I will describe an interesting algebraic phenomenon which seems to play an important role in applications theory: roughly, irreducible representations retain a form of irreducibility after microlocalizing. Our main motivation is a problem in analytic number theory (bonding L-functions) which I'll also discuss. No background in microlocal analysis (and very little representation theory) will be assumed.