On the number of nodal domains of toral eigenfunctions

Seminar series

Number Theory Seminar

Date

Thu, 10 Mar 2016

Time

16:00 - 17:00

Location

Speaker

Igor Wigman

Organisation

King's College London

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.