Nodal Statistics for Graphs and Matrices

Series
Atlanta Combinatorics Colloquium
Time
Thursday, April 3, 2025 - 5:00pm for 1 hour (actually 50 minutes)
Location
Bill Moore SSC Press Room A
Speaker
John Urschel – Massachusetts Institute of Technology – urschel@mit.eduhttps://math.mit.edu/~urschel/
Organizer
Tom Kelly

The study of nodal statistics provides insight into the spectral properties of graphs and matrices, drawing strong parallels with classical results in analysis. 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 in the continuous setting. In addition, we will discuss some recent progress towards a complete understanding of the extremal properties of the nodal statistics of a matrix.