Analysis Seminar

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

In joint work with Malabika Pramanik (U. British Columbia), I will present in the second part of my lecture a result on the 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 restriction results of Burq-Gérard-Tzvetkov ’06.

Event contact: hazel dot mcknight at rochester dot edu