Gårding prize lecture, Pär Kurlberg (KTH): "Repulsion in number theory and physics"
Plats: MH:Gårding. You can also follow the lecture via zoom. Please contact the organizer for the link.
Kontakt: erik [dot] wahlen [at] math [dot] lu [dot] se
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This is the first in a series of two lectures with the Gårding prize recipients of 2021. The second lecture will be given by Andreas Strömbergsson (Uppsala University) in January.
Zeros of the Riemann zeta function and eigenvalues of quantized
chaotic Hamiltonians appear 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 R3/Z3. 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.