Date
Speaker
Title and Abstract
Semptember 25
October 9
Title: Gaps between zeros of zeta and L-functions of high degree
Abstract: There is a great deal of evidence, both theoretical and experimental, that the distribution of zeros of zeta and L-functions can be modeled using statistics of eigenvalues of random matrices from classical compact groups. In particular, we expect that there are arbitrarily large and small normalized gaps between the ordinates of (high) zeros zeta and L-functions. Previous results are known for zeta and L-functions of degrees 1 and 2. We discuss some new results for higher degrees, including Dedekind zeta-functions associated with Galois extensions of and principal automorphic L-functions.
October 23
Title: Frobenius-Schur Indicator
Abstract: Given an irreducible complex representation (R,V) of a finite group G, Frobenius and Schur, around 1900, introduced an invariant for answering the question of when R is real, that is, when there is a basis of V such that the associated matrix of R(g) has real entries for all g in G. The invariant is now known as the Frobenius-Schur indicator. This talk will be conceptual to understand this invariant with some examples.