**CANCELLED**
Tristan Freiberg, Department of Pure Mathematics, University of Waterloo
“Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers”
We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors–Keating and Smilansky, we formulate an analog of the Hardy–Littlewood prime k-tuple conjecture for sums of two squares, and show that it implies that the spectral gaps, after removing degeneracies, are Poisson distributed. Consequently, by work of Rudnick and Uebersch ̈ar, the level spacings of arithmetic toral point scatterers, in the weak coupling limit, are also Poisson distributed. We also give numerical evidence for the conjecture and its implications.
This is joint work with P ̈ar Kurlberg and Lior Rosenzweig.
MC 5479