# Christopher Sogge: Mini course on Eigenfunction and quasimode estimates

**Time: **
Mon 2019-03-25 10.00 - 14.00

**Lecturer: **
Christopher Sogge, Johns Hopkins University

**Location: **
Seminar Hall Kuskvillan, Institut Mittag-Leffler

Abstract: We shall go over recent bounds for eigenfunctions on compact Riemannian manifolds obeying certain geometric assumptions, especially curvature assumptions. We shall investigate the types of concentration that can occur and also discuss bounds for perturbations involving very singular potentials. The latter involve potentials \(V\) which are in \(L^{n/2}\) and also in the Kato class.

We shall show that the estimates may break down for potentials not obeying these assumptions. We shall also address bounds for Bochner-Riesz operators arising from Schrödinger operators with singular potentials and related problems.