Michael Harris, Department of Mathematics, Columbia University Abstract:  The talk will be an introduction to the Langlands program and to some of the preoccupations of contemporary algebraic number theory.I will concentrate on the recent breakthrough of Vincent Lafforgue in defining a Langlands correspondence for reductive…

Matt Baker, Department of Mathematics, Georgia Tech Abstract: A pasture is, roughly speaking, a field in which addition is allowed to be both multivalued and partially undefined. I will describe a theorem about univariate polynomials over pastures which simultaneously generalizes Descartes’ Rule of Signs and the theory of…