Colloquium – Talk by Dr. John Urschel: October 23, 2025
October 23, 2025 (Thursday), 4:10 pm
Dr. John Urschel, Massachusetts Institute of Technology
Nodal Statistics for Graphs and Matrices
The study of discrete nodal statistics, that is, data regarding the zeros of Laplacian eigenvectors, provides insight into structural properties of graphs and matrices, 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 domains and nodal counts 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.
This is based on serval joint works with various collaborators: Maksym Radziwill, Chantal David, Alia Hamieh, and Hua Lin.