Jens MARKLOF, Bristol
"Energy level statistics, lattice point problems, and ergodic theory"
One of the central challenges in quantum chaos is to establish to what
extent the energy levels of quantized integrable systems behave
statistically like independent random variables from a Poisson process.
This lecture series will
-explain how to measure the "randomness" of a given point sequence,
-illustrate the connection of questions in quantum chaos with certain
lattice point problems and the theory of distribution modulo one, and
-provide an introduction to Ratner's theorem on the classication of
measures invariant under unipotent flows, and show how it can be
employed to solve (at least some aspects) of the above lattice point
problems.
The lectures with be aimed at a non-specialist audience.