Dmitry Beliaev: Random plane waves and the critical percolation

Abstract: Random plane waves are the universal model for high energy eigenfunctions of the Laplacian in domains with chaotic dynamics. We are interested in the geometry of the nodal lines (zero set) and nodal domains of the random plane wave. In this talk I will explain why this is an interesting model, present some classical and recent results and finally will discuss the conjectured connection between the random wave model and critical percolation. The talk should be accessible to the general audience, in particular no prior knowledge about the random plane wave model or percolation is required.