On the geometry and topology of zero sets of Schrödinger eigenfunctions

Spectral Geometry Seminar
Topic:On the geometry and topology of zero sets of Schrödinger eigenfunctions
Speaker:Yaiza Canzani
Affiliation:Member, School of Mathematics
Date:Monday, March 30
Time/Room:3:30pm - 4:30pm/S-101

In this talk I will present some new results on the structure of the zero sets of Schrödinger eigenfunctions on compact Riemannian manifolds. I will first explain how wiggly the zero sets can be by studying the number of intersections with a fixed curve as the eigenvalue grows to infinity. Then, I will discuss some results on the topology of the zero sets when the eigenfunctions are randomized. This talk is based on joint works with John Toth and Peter Sarnak.