On the number of nodal domains of toral eigenfunctions

Analysis Seminar
Topic:On the number of nodal domains of toral eigenfunctions
Speaker:Igor Wigman
Affiliation:King's College, London
Date:Tuesday, April 19
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/analysis/2016/0419-Wigman

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin's results for random fields and Bourgain's de-randomisation procedure we establish a precise asymptotic result for "generic" eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions. This work is joint with Jerry Buckley.