Jerry Buckley (King's College London)
On the number of nodal domains of toral eigenfunctions.
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. Joint work with Igor Wigman.