Dmitry Belyaev (Oxford): Probabilistic view of high-energy eigenfunctions of the Laplacian
Abstract: Study of high-energy eigenfunctions of the Laplacian is a classical and notoriously difficult subject. It has been conjectured by M. Berry that they could be modelled by a random superposition of plane waves. This means that a random function provides a good model for a “typical” function. One of the benefits of this approach is that it allows to use both probabilistic and analytic methods to study these random functions. I will give an overview of the field and explain the recent progress in the study of smooth Gaussian functions and their geometric properties.