On the number of nodal domains of toral eigenfunctions

10 March 2016
16:00
Igor Wigman
Abstract

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.

  • Number Theory Seminar