Analysis and Applications research seminar: Concentration and Growth of Laplace Eigenfunctions
- Date: Wednesday 6 November 2019, 16:30 – 17:30
- Location: Roger Stevens LT 11 (10.11)
- Type: Analysis and Applications, Seminars, Pure Mathematics
- Cost: Free
Dr Jeff Galkowski (UCL) will present his research in Analysis and Applications.
In this talk, he will discuss a new approach to understanding eigenfunction concentration. He will 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. He will also show that the phenomenon behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, he will use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.