The APDE seminar on Monday, 03/16 will be given by Johannes Sjöstrand in Evans 939 from 4:10 to 5pm.

Title: Resonances over a potential well in an island.

Abstract: Recent work with M. Zerzeri. Let V : R^n → R be a sufficiently analytic potential which tends to 0 at infinity. Assume that for an E > 0 we have V^{-1}(]- ∞ ,E[)=U(E) ⊔ S(E), where U(E) ∩ S(E) = ∅ , with U(E) connected and bounded (the well) and S(E) connected (the sea). The distribution of the resonances of -h^2 Δ + V near E has been thoroughly studied since more than 30 years. If we increase E a natural scenario is that the decomposition persists until the closures of U(E) and S(E) intersect at a critical energy E = E_0. Under some natural assumptions we show that near E_0 most of the resonances are close to the real axis and obey a Weyl law. In one dimension there are more detailed results (Fujiie-Ramond ’98).