QLunch: Nodal Sets of Random Spherical Harmonics

Speaker: Mikhail Sodin, Tel Aviv University

Title: Nodal Sets of Random Spherical Harmonics

Abstract: In the talk I will describe what is known and (mostly) unknown about asymptotic statistical topology of zero sets of random spherical harmonics of large degree on the two-dimensional sphere. I will start with basic open questions and then will discuss a non-trivial lower bound for the variance of the number of connected components of the zero set recently obtained with Fedor Nazarov. Our argument can be viewed as, probably, the first (though, modest) rigorous support of the beautiful Bogomolny-Schmit heuristics, which connects the asymptotic nodal counting with a percolation model on the square lattice.