Abstract: The philosophy of Kostant and Kirillov seeks to find a relationship between two seemingly disparate sets: the family of unitary representations of a Lie group $G$ and a set of symplectic manifolds lying in $\mathfrak{g}^*$. Perhaps surprisingly, there is a natural bijection between them when $G$ is nilpotent, and significant progress has even been made in the setting of semisimple Lie groups. We will discuss what is left to be done, and why the answer will involve some beautiful combinatorics.

Refreshments will be served compliments of the Division of Mathematics & Natural Science.