COMPUTATIONAL MATH – IDeAS SEMINAR Recurring weekly series · Thursdays · 224 Fine Hall ** NOTE: Earlier time than previous weeks ** This week's talk: Speaker: Tom Trogdon (University of Washington) Title: Towards PCA without the SVD: Lanczos-based spike detection Date: Thursday, April 23, 2026 Time: 1:30 PM – 2:30 PM (note earlier time) Room: 224 Fine Hall Abstract: This talk will give an overview of the study of algorithms on random data, and in particular, algorithms from numerical linear algebra (NLA) on random matrices. The combination of ideas from numerical linear algebra and random matrices goes back, at least, to the seminal work of Goldstine and von Neumann. The works of Trotter, Silverstein, Edelman, Dumitriu & Edelman, Pfrang, Deift & Menon, and many others, developed these ideas further. A core subset of NLA algorithms, the Krylov subspace methods, play particularly well with existing random matrix theory. Through the study of random orthogonal polynomials, as perturbations of deterministic orthogonal polynomials, the concentration phenomenon in these methods can be explained using local laws from random matrix theory. We will use these ideas, and methods, to efficiently and robustly perform spike detection in the spiked sample covariance model and move towards PCA without the SVD. About the speaker: Thomas Trogdon is a Professor and Chair of Applied Mathematics, an adjunct professor in the Department of Mathematics and an affiliate of the Algorithmic Foundations of Data Science Institute, all at the University of Washington. Trogdon works on a variety of computational, applied and theoretical problems from the fields of mathematical physics, random matrix theory and approximation theory. He was an NSF Postdoctoral Fellow at the Courant Institute at NYU from 2013-2016, and he won the SIAM Richard C. DiPrima Prize in 2013. Then he joined the Department of Mathematics at UC Irvine and won the 2017 SIAM Gábor Szegő Prize before he joined the University of Washington in 2019. Up next: Thursday, April 30 – Boris Landa (Yale University). There are a few slots to meet with the speakers, please let us know if you would like one (gilles@princeton.edu). - Liza Rebrova, Marc Aurèle Gilles, and Jorge Garza Vargas.