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.