#
Chaire André Aisenstadt Chair

# 2003-2004

Une série de conférences

A series of lectures

PROF. PETER SARNAK

(biographical notes biographiques)

Princeton University

#####
Centre de recherches mathematiques

Universite de Montreal

Pavillon Andre-Aisenstadt

2920, chemin de la Tour

Salle / Room 6214

"The spectrum of the modular surface"

Le mardi, 4 mai 2004, 16h00 / Tuesday, May 4, 2004, 4:00 pm

We review what is known about the spectrum of the Laplacian on the modular surface

and why it is of interest.

Une reception suivra la conférence au Salon Maurice-l'Abbe, salle 6245

There will be a reception after the lecture in Salon Maurice-l'Abbe, Room 6245

## "Classical versus quantum fluctuations on the modular surface"

Le mercredi, 5 mai 2004, 15h00 / Wednesday, May 5, 2004, 3:00 pm

A general "conjecture" by physicists concerning the relation between the quantum and classical fluctuations of observables is analyzed for the modular surface. It turns out that the conjecture is false in this case and that its discrepancy from the truth is a subtle arithmetic invariant.

## "Extrema of Epstein's zeta function"

Le jeudi, 6 mai 2004, 15h00 / Thursday, May 6, 2004, 3:00 pm

The extrema of the Epstein Zeta function for a fixed value of s is of interest in the theory heights, lattice packings of space... In dimension 2, Rankin and Cassels deterimined the local minimum. We discuss the higher dimensional case and in particular the use of the full ring of invariant differential operators.