The Math Department Colloquium features talks from research mathematicians aimed at a wide audience.
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John Urschel (MIT)
Title:Nodal Statistics for Graphs and Matrices
Abstract: 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.
About the Speaker: John Urschel is the Class of 1956 Career Development Assistant Professor of Mathematics at MIT. Previously, he was a member of the Institute for Advanced Study and a Junior Fellow at the Harvard Society of Fellows. He received his Ph.D. in Mathematics from MIT in 2021 under the supervision of Michel Goemans. His main research interests include matrix analysis, numerical linear algebra, and spectral graph theory. He recently received the SIAM DiPrima Prize and the SIAM Early Career Prize in Linear Algebra.
Date: Thursday, September 25, 2025
Time: 12:00 PM - 1:00 PM
Location: MH-476 or via Zoom (register for link)
Zoom registration for attending virtually: bit.ly/amc-f25-urschel