On the number of nodal domains of toral eigenfunctions

On the number of nodal domains of toral eigenfunctions - Igor Wigman

Igor Wigman
King's College, London
April 19, 2016
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.