Yann Chaubet (Cambridge University)
The modified Lax-Phillips conjecture for analytic obstacles
Abstract:
This talk will be centered on the scattering resonances of the Dirichlet Laplace
operator acting in the exterior of a collection of obstacles of the Euclidian
space. In the end of the 80’s, Ikawa conjectured that there should be a band
with an infinite number of such resonances, as soon as the obstacles are
trapping. This is the so-called modified Lax-Phillips conjecture (MLPC). After a
short state of the art on this question, I will present some recent results
which answer positively to the MLPC for analytic obstacles. I will briefly
explain the method of proof, based on Ikawa’s criterion, which involves certain
dynamical series; the latter series are studied through the prism of
Pollicott-Ruelle resonances. This is a joint work with Vesselin Petkov.