Colloquium Series

Fall 2025

October 17, 2025

Margaret Beck, Boston University

Topic: Topological Implications for Stability
Time: 4:00-5:00 pm
Location: JCC265
Reception: JCC501
Abstract: In the context of many PDEs, the stability of a solution roughly corresponds to whether or not that solution can be expected to be observed in the long-time dynamics of the system. Determining stability often amounts to understanding the point spectrum, or eigenvalues, of an associated linear differential operator, with positive-real-part eigenvalues indicating an instability. In this talk, we will discuss recent work connecting the topological properties that govern the existence of the solution with the existence of positive eigenvalues and instability. 

September 5, 2025

John Urschel, MIT

Topic: Nodal Statistics for Graphs and Matrices
Time: 4:00-5:00 pm
Location: JCC265
Reception: JCC501
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.