KTH/SU Mathematics Colloquium
05-04-13
Zeév Rudnick, Tel Aviv University
Eigenvalue statistics and lattice points
One of the more challenging problems in spectral theory and
mathematical physics today is to understand the statistical
distribution of eigenvalues of the Laplacian on a compact
manifold. Among the most studied quantities is the counting function
for eigenvalues in a window [E,E+S], with the position E of the window
chosen at random and the window size S=S(E) depending on its
position. I will describe what is known about the statistics of this
counting function for the very simple case of the flat torus, where
the problem reduces to counting lattice points in annuli.