Collection Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Organizer(s)
Date(s)
23/04/2024
Statistics of randomized Laplace eigenfunctions
There are several questions about the behavior of Laplace eigenfunctions that are extremely hard to tackle and hence remain unsolved. Among the features that we don’t fully understand yet are: the number of critical points, the size of the zero set, the number of components of the zero set, and the topology of such components. A natural approach is then to randomize the problem and study these features for a randomized version of the eigenfunctions. In this talk I will present several results that tackle the problems described above for random linear combinations of eigenfunctions (with Gaussian coefficients) on a compact Riemannian manifold. This talk is based on joint works with Boris Hanin and Peter Sarnak.
