Quantum Chaos on hyperbolic surfaces

Graduate course, Spring 2017
20 hours

Location: Howard House, 4th floor seminar room

Time: Monday 11am - 1pm


Quantum chaos can be thought as the study of quantum systems for which the corresponding classical dynamics is chaotic. In this course we will introduce this theory via the study of the spectrum and eigenfunctions of the Laplacian on hyperbolic surfaces. This setting connects ergodic theory, number theory (automorphic forms) and mathematical physics and is at the centre of current active research. The ultimate goal would be to understand the Arithmetic Quantum Unique Ergodicity theorem of Lindenstrauss, and its connection to eigenfunctions on discrete regular graphs. There will be minimal prerequisites, basic analysis and algebra should be sufficient.




Lecture notes

Quantum chaos on hyperbolic surfaces (pdf) (last update 04.04.2017)