October 31, 2023
Title: Repulsion in number theory and physics
Speaker: Pär Kurlberg (KTH)
Zeros of the Riemann zeta function and eigenvalues of quantized chaotic Hamiltonians appears to have something in common. Namely, they both seem to be ruled by random matrix theory and consequently should exhibit "repulsion" in the sense that small gaps between elements are very rare. More mysteriously, while zeros of different L-functions (i.e., generalizations of the Riemann zeta function) are "mostly independent" they also exhibit subtle repulsion effects on zeros of other L-functions.
We will give a survey of the above phenomena. Time permitting we will also discuss repulsion between eigenvalues of "arithmetic Seba billiards", a certain singular perturbation of the Laplacian on the 3D torus R^3/Z^3. The perturbation is weak enough to allow for arithmetic features from the unperturbed system to be brought into play, yet strong enough to provably induce repulsion.