School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

King's College, London

Using the spectral multiplicities of the standard torus, we endow the Laplace

Abstract:

eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian

Laplace eigenfunctions on the torus (“arithmetic random waves”). We study the distribution

of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is

that the asymptotics for the variance is non-universal, and is intimately related to the arithmetic

of lattice points lying on a circle with radius corresponding to the energy.

This work is joint with Manjunath Krishnapur and Par Kurlberg.

Coffee will be served at 12:00 before the lecture

at Schreiber building 006