Session S33 - Spectral Geometry

Monday, July 12, 13:00 ~ 13:20 UTC-3

Geodesic beams and Weyl remainders

Jeffrey Galkowski

University College London, United Kingdom   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we discuss quantitative improvements for Weyl remainders under dynamical assumptions on the geodesic flow. We consider a variety of Weyl type remainders including asymptotics for the eigenvalue counting function as well as for the on and off diagonal spectral projector. These improvements are obtained by combining the geodesic beam approach to understanding eigenfunction concentration together with an appropriate decomposition of the spectral projector into quasimodes for the Laplacian. One striking consequence of these estimates is a quantitatively improved Weyl remainder on all product manifolds.

Joint work with Yaiza Canzani (University of North Carolina at Chapel Hill, United States).

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