*
Recently, there has been a lot of interest in connections
between quantum chaos and number theory. I will talk about the
holomorphic quantum unique ergodicity conjecture and in particular,
describe joint work with Paul Nelson and Ameya Pitale where we settle
this conjecture in all aspects (for classical modular forms of trivial
nebentypus). More precisely, let f be a classical holomorphic newform
of level q and even weight k. We prove that the pushforward to the
full level modular curve of the mass of f equidistributes as qk goes
to infinity. This generalizes previous work by
Holowinsky-Soundararajan (the case q=1, k-> infinity) and Nelson (the
case qk -> infinity over squarefree
integers q). A potentially surprising aspect of our work is that we
obtain a power savings in the rate of equidistribution as q becomes
sufficiently ``powerful'' (far away from being squarefree), and in
particular in the ``depth aspect'' as q traverses the powers of a
fixed prime.*

Donnerstag, den 8. November 2012 um 17 c.t. Uhr, in INF 288, HS2 Donnerstag, den 8. November 2012 at 17 c.t., in INF 288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Kohnen