Title: p-adic groups, symmetric spaces, and their representation theory'
Abstract: We give an introduction to representation theory of p-adic groups.
After a few lectures in the beginning on parabolic induction and Jacquet modules
and the role of supercuspidal rep's in representation theory of p-adic groups,
we will discuss analogous development for `relative' aspects of the subject in which we have a reductive group G together with an involution \theta on G with H, the fixed points of \theta, and the question we try to answer is if we can classify all representations of
G which carry an invariant linear form for the subgroup H in terms of
relative supercuspidal rep's. (The representations of G which carry an H invariant
linear form are said to be distinguished.)
Title: L-functions and Random Matrix Theory
Abstract: we will give an introduction to the theory of the Riemann zeta function and the more general zoo of L-functions.
We will describe the random matrix model, according to which statistical properties of L-functions correspond to the statistical properties of characteristic polynomials of random matrices drawn from certain classical groups. We will discuss the empirical and heuristic evidence for this model as well as existing partial results. We will see how function field analogues and representation theory can shed light on the mysterious connection between L-functions and random matrices.
Title: Multiple Dirichlet series and number theory
Abstract: We'll present a survey of some recent work on Dirichlet series in several complex variables. Examples will be given from the theory of automorphic forms, prehomogeneous vector spaces and subgroup growth.