"Resonances for (open) Quantum Maps"

 Quantum maps are obtained by quantizing canonical
transformations on compact symplectic manifolds, such
as the 2-torus. They are a popular model in physics as
they posess many features of quantum systems with
interesting underlying classical mechanics.

 Open quantum maps arise when we model scattering,
in particular with chaotic classical dynamics.
Quantum resonances make a natural appearance and
in some cases we can prove results inaccessible in more
standard models based on Schr\"odinger equations or
obstacle scattering. In particular we can see the
fractal Weyl laws for the number of resonances.

 This is joint work with Stephane Nonnenmacher of
{\em Commissariat  \`a l'Energie Atomique}