Abstract 

In this talk, I will discuss several new results on non-concentration of Neumann eigenfunctions in shrinking neighborhoods of planar domains. The main result is a sharp estimate in a neighborhood of a corner point, but I will also discuss some other results in smoother situations. The main tools are a Rellich commutator argument and an induction argument to control boundary error terms. This is joint work with John Toth.

About the speaker 

I am a Professor at UNC, studying semiclassical analysis and partial differential equations. I am part of the UNC Analysis and PDE research group which is funded in part by NSF RTG grant DMS-2135998 “Partial Differential Equations on Manifolds”.