Zeev Rudnick

Title:Topics in Arithmetic Quantum Chaos
Abstract:I will give an introduction to a collection of recent results and conjectures on the spectrum and the eigenfunctions of the Laplacian, with emphasis on arithmetic models. No prior knowledge will be assumed.
Among the topics discussed will be:
  • The universality conjectures for spectral statistics and relations with the classical subjects of uniform distribution and lattice point problems, zeros of zeta functions and Random Matrix Theory.
  • Nodal lines of eigenfunctions of the Laplacian and lattice points on circles and spheres.