Roman Holowinsky (Toronto)

The Rudnick-Sarnak Conjectures

We'll discuss the quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak as well as various analogous equidistribution statements. The QUE problem comes from an area of physics known as quantum chaos and provides connections between classical dynamical systems and their quantum models. Certain dynamical systems associated with negatively curved arithmetic surfaces have strong connections with number theory. We'll describe this number theoretic setting and provide a brief sketch as to how one may prove QUE in these cases.