Seminar

Quantum affine Lie algebras and Gl(n) over non-Archimedean local fields

We will discus the relationship between the representation theory of quantum affine Lie algebras and that of groups of matrices over non-Archimedean local fields, such as the p-adic numbers. In particular, we will address the question of when the tensor of two simple representations of a quantum affine lie algebra is simple and the corresponding question of when the parabolic induction of two simple representations of p-adic matrices is simple.

Counting Number Fields

Abstract: We will discuss some recent techniques that have been successful in counting a variety of objects in number theory. Our main focus will be on counting low degree number fields, following the inspirational work of Bhargava. We will see many areas of mathematics come together in this story.