Applied Mathematics and Applied Physics

Applied Mathematics Colloquium

Jeremy Marzuola
Applied Mathematics, Columbia University

"Eigenfunction concentration for polygonal billiards"

With Andrew Hassell and Luc Hillairet, we extend the results on eigenfunction concentration in billiards as proved by the speaker in an earlier work. There, the methods developed in the works of Burq-Zworski to study eigenfunctions for billiards which have rectangular components were applied. Here we take an arbitrary polygonal billiard B and show that eigenfunction  mass cannot concentrate away from the vertices; in other words, given any neighborhood U of the vertices, there is a lower bound

∫_U|u|²  ≥ c ∫_B |u|²

for some c = c(U) > 0 and any eigenfunction u.

Host: Guillaume Bal