Title: Concentration and Growth of Laplace Eigenfunctions
Speaker: Jeffrey Galkowski
Speaker Info: Northeastern
Brief Description:
Special Note: Note special time and date
Abstract:
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 high $L^p$ norms and Weyl laws; in each case obtaining quantitative improvements over the known bounds.Date: Tuesday, January 22, 2019