Thursday, 10th March 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

Zeev Rudnick

(Tel Aviv University)

"Eigenvalue statistics and lattice points"

** Abstract: **

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.

Light refreshments will be served in the faculty lounge at 3:30.

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