# Recent progress on the Yau and Nadirashvili conjecture concerning the volumes of the zero sets of Laplacian Eigenfunctions

Recent progress on the Yau and Nadirashvili conjecture concerning the volumes of the zero sets of Laplacian Eigenfunctions

Organizers: Eugenia Malinnikova and Mikhail Sodin

Participants: Lev Buhovski, Hamid Hezari, Fang Hua Lin, Alexander Logunov, Dan Mangoubi, Fedor Nazarov, Melissa Tacy, John Toth, Steve Zelditch

Outcomes

D Mangoubi Lecture Harmonic functions - positivity and convexity

J Toth Lecture The nodal intersection problem for Laplace eigenfunctions

E Malinnikova Lecture An improvement of Liouville theorem for discrete harmonic functions

M Sodin Lecture Nodal sets of random spherical harmonics

S Zelditch Lecture Log lower bound on the number of nodal domains on some surfaces of negative curvature

M Tacy Lecture Equidistribution of random waves on shrinking balls