The global aim of quantum chaos is to understand the spectral and dynamical properties of quantum systems, which can be related in some limit to a classical dynamical system. The behaviour of the latter may range from very regular to very chaotic.

Specifically, quantum chaos tries to identify the imprint of this classical dynamics on the quantum side. For instance, the following spectral data has received much attention:

• the local spectral statistics of the quantum system, namely the Poisson vs. Random Matrix Theory conjectures. Long range statistics seem to be easier to study at a rigorous level, and may also provide valuable information.

• the spatial structure of the eigenstates (or quasimodes): bounds on their Lp norms, classification of semiclassical limit measures. On the (microscopic) scale of the wavelength, the structure of the nodal sets has recently attracted a lot of attention.

• relations between chaotic and random objects.

The workshop will gather specialists working on various types of models, ranging from arithmetic manifolds to quantum graphs or quantum maps. Although they share a common global aim, the methods of analysis may be very model dependent, borrowing from various fields of mathematics. These different models/methods will also hint at the following recurring question: which spectral properties are universal, as opposed to being specific to a restricted class of models?

### Scientific Organizers

- N. Anantharaman (Centre de Mathématiques Laurent Schwartz - Ecole Polytechnique)
- S. Nonnenmacher (CEA/Saclay, SPhT, France)

- Z. Rudnick (Tel-Aviv)
- S. Zelditch (Johns Hopkins)