05C50 Online Seminar: John Urschel

Given a symmetric matrix with a given sign pattern, what can the sign patterns of its eigenvectors look like? This simple question is closely related to the study of discrete nodal statistics, and draws strong parallels with classical results in analysis for Laplacian eigenfunctions. In this talk, we will give an overview of the field, covering key results on nodal sets for graphs and their connection to known results and open problems in the continuous setting. In addition, we will discuss some recent progress towards a more complete understanding of the extremal properties of the nodal statistics of a matrix.