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Examples of the structure and dispersion of waves on two-dimensional cones

Seminar: Bay Area Microlocal Analysis Seminar | December 7 | 4:10-5 p.m. | 891 Evans Hall


Austin Ford, Stanford University

Department of Mathematics


In recent years, there has been much effort to understand the dispersive properties of solutions to the wave and Schrodinger equations in various geometries. I will discuss in this talk the beginnings of extending this program to singular spaces, namely the settings of two-dimensional cones and related spaces. This will begin with the asymptotics of the Schrodinger group, and I will show how these lead to dispersive and Strichartz estimates for solutions to this equation on cones. I will also discuss joint work with Matt Blair, Sebastian Herr, and Jeremy Marzuola extending these estimates to solutions on polygonal domains and surfaces with (exact) conical singularities. The analogous results for solutions to the wave equation on these spaces will also be discussed (joint with Matt Blair and Jeremy Marzuola). Time permitting, I'll also mention current work with Andrew Hassell and Luc Hillairet with the goal of understanding the microlocal structure of these "classical waves" and the various implications knowing this structure would have.


zworski@math.berkeley.edu