Talk Abstracts

We study a quantum and classical correspondence related to the Strichartz estimates. First we consider the orthonormal Strichartz estimates on manifolds with ends. Under the nontrapping condition we prove the global-in-time estimates on manifolds with asymptotically conic ends or with asymptotically hyperbolic ends. Then we show that, for a class of pseudodifferential operators including the Laplace-Beltrami operator on the scattering manifolds, such estimates imply the global-in-time Strichartz estimates for the kinetic transport equations in the semiclassical limit. As a byproduct we prove that the existence of a periodic stable geodesic breaks the orthonormal Strichartz estimates. An interesting point in the proof is that we do not need any quasimode.