# Approximating flats by periodic flats in CAT (0) square complexes

# Every group is an outer automorphism group of a finitely generated group

### Publication Type:

Journal Article### Source:

J. Pure Appl. Algebra , Volume 200, Issue 1-2, p.137-147 (2005)# The coherence of one-relator groups with torsion and the hanna Neumann conjecture

### Publication Type:

Journal Article### Source:

Bull, London Math. Soc., Volume 37, Issue 5, p.697-705 (2005)# The Tits alternative for CAT(0) cubical complexes

### Publication Type:

Journal Article### Source:

Bull, London Math. Soc., Volume 37, Issue 5, p.706-710 (2005)# Counting multiple cyclic choices without adjacencies

### Publication Type:

Journal Article### Source:

Canad. Math. Bull., Volume 48, Issue 2, p.244-250 (2005)# The transition from geostrophic to stratified turbulence.

### Publication Type:

Journal Article### Source:

J. Fluid Mech., Volume 568, p.89-108 (2006)# Modular forms, quaternion algebras, and special values of L-functions

### Publication Type:

Thesis### Source:

Mathematics and Statistics, McGill University, p.79 (1997)### Abstract:

Let f be a cusp form of weight 2 and level N. Let K be an imaginary quadratic field of discriminant - D, and d an ideal class of K. We obtain precise formulas for the special values of the L-functions associated to the Rankin convolution off and a theta series associated to the ideal class A, in terms of the Petersson scalar product of f with the theta series associated to an Eichler order in a positive definite quaternion algebra. Our work is an extension of the work done by Gross [7] il. The central tools used in this thesis are Rankin's method and a reformulation of Gross of work of Waldspurger concerning central critical values.# Single energy multiscale analysis and Anderson localization

05/24/2007 - 14:40

05/24/2007 - 15:40

Speaker:

Francois Germinet (Univ. Cergy-Pontoise, Paris)

Location:

CRM, Room 5340

Abstract:

In the talk, I will show how to extract exponentially decaying eigenfunctions out of the basic and standard single energy multiscale analysis introduced by Frohlich and Spencer in 1983. There will be much more.

# Regularity of solutions in the calculus of variations

05/28/2007 - 13:30

Speaker:

Francis Clarke (Institut universitaire de France et Universite de Lyon, etc)

Location:

CRM, Room 5340

Abstract:

An overview of some classical and recent results on the regularity of solutions in the (single and multiple integral) calculus of variations. Along the way are reviewed the celebrated theorems of Hilbert-Haar and De Giorgi.

# Nodal lines for random eigenfunctions of the Laplacian on the torus

05/24/2007 - 11:00

05/24/2007 - 12:00

Speaker:

Igor Wigman (CRM and McGill)

Location:

CRM, Room 5340

Abstract:

We study the volume of nodal sets for eigenfunctions of the Laplacian on the standard torus in two or more dimensions. We consider a sequence of eigenvalues with growing multiplicity , and compute the expectation and variance of the volume of the nodal set with respect to a Gaussian probability measure on the eigenspaces. We show that the expected volume of the nodal set is . Our main result is that the variance of the volume normalized by is bounded by , so that the normalized volume has vanishing fluctuations as we increase the dimension of the eigenspace.