### 06.07.2018 12:00 Rupert Frank (LMU):Localization of orthonormal functions in spectral clustersB 133 (Theresienstr. 39, 80333 München)

We generalize the $$L^p$$ spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. We show that these bounds are optimal on any manifold in a very strong sense. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators and their optimality follows by semi-classical analysis. The talk is based on joint work with Julien Sabin.