Speaker
Maurizia Rossi
(Università degli Studi di Milano-Bicocca)
Description
In this talk we investigate the behavior of the "typical" Laplacian eigenfunction of a compact smooth Riemannian manifold. In particular, motivated by both Yau's conjecture on nodal sets and Berry's ansatz on planar random waves, we consider Gaussian eigenfunctions on the sphere and study the distribution of the length of their nodal lines in the high energy limit. This result raises several questions regarding both the distribution of other geometric functionals and the behavior of nodal statistics of random eigenfunctions on a "generic" manifold. (This talk is mainly based on a joint work with D. Marinucci and I. Wigman.)
Author
Maurizia Rossi
(Università degli Studi di Milano-Bicocca)