Andrea Sartori

Asymptotic nodal length and log-integrability of toral eigenfunctions

Yau conjectured that the nodal length, volume of the zero set, of Laplace eigenfunction on smooth compact manifolds should be comparable to the square root of their eigenvalue. Going further, should we also expect an asymptotic law for the nodal length? In this talk I will focus on Laplace eigenfunctions on the 2d torus and discuss how their “special” spectral properties allowed us to find the asymptotic behavior of their nodal length both at large and small scales.