(May 25) Tonghai Yang: Existence of algebraic Hecke characters - In this talk, we will explain that a weak version of the Brumer-Stark conjecture is equivalent to the existence of certain algebraic Hecke characters, which can be viewed as generalization of the Weil's Jacobi characters. As a consequence, we show that the Brumer-Stark conjecture in CM cases implies the Brumer-Stark conjecture in general.

(May 25) Douglas Ulmer: On the maximum rank of an elliptic curve as a function of its conductor - It is widely believed that there are elliptic curves over Q with Mordell-Weil group of arbitrarily large rank. We prove an analogous statement for elliptic curves over function fields of curves over finite fields. In contrast to an earlier example of Shafarevitch and Tate, our curves are "non-isotrivial," i.e., they have non-constant j-invariant. We also discuss bounds suggested by our example for the rank of an elliptic curve in terms of its conductor.