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.