Analysis and PDE Seminar: Concentration and Growth of Laplace Eigenfunctions

Seminar | May 20 | 4:10-5 p.m. | 740 Evans Hall

 Jeffrey Galkowski, Northeastern University

 Department of Mathematics

In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^2$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration including Weyl laws; in each case obtaining quantitative improvements over the known bounds.