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Department of Mathematics,
University of California San Diego

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Math 248 - Analysis Seminar

Jeffrey Galkowski

Northeastern Univ.

Concentration and Growth of Laplace Eigenfunctions

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.

Host: Jacob Sterbenz

January 31, 2019

10:00 AM

AP&M 7321

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