# Analysis Seminar

## $L^p$ restriction of eigenfunctions to random Cantor-type sets

Suresh Eswarathasan, McGill University and Dalhousie University

Friday, November 22nd, 2019
2:00 PM - 3:00 PM
Hylan 1106A

Let $(M,g)$ be a compact Riemannian n-manifold without boundary. Consider the corresponding $L^2$-normalized Laplace-Beltrami eigenfunctions. In the first part of the lecture, I will give a survey of results which demonstrate how the geometry of $M$ affects the behaviour of these special functions, particularly their “size” which can be quantified by estimating $L^p$ norms.

In joint work with Malabika Pramanik (U. British Columbia), I will present in the second part of my lecture a result on the $L^p$ restriction of these eigenfunctions to random Cantor-type subsets of M. This, in some sense, interpolates between the standard eigenfunction bounds of Sogge ‘88 and the smooth submanifold $L^p$ restriction results of Burq-Gérard-Tzvetkov ’06.

Event contact: hazel dot mcknight at rochester dot edu