# Bounds for spectral projectors on Riemannian manifolds

The HADES seminar on Tuesday, April 26 will be at 3:30 pm in Room 740.

Speaker: Pierre Germain

Abstract: On a Riemannian manifold, consider the spectral projector on a thin spectral band $[\lambda , \lambda + \delta]$ for the Laplace-Beltrami operator. What is its operator norm from $L^2$ to $L^q$? Or, to put it in semiclassical terms, how large can the $L^p$ norm of a quasimode normalized in $L^2$ be? This is a fascinating problem, which is closely related to a number of fundamental analytic questions. I will try and describe what is known, and some recent progress that have been made. There will be some overlap with my talk at the Analysis seminar, but not much.