Speaker: Yi Han (MIT)Title: Some progress and mysteries in the study of inhomogeneous random matricesAbstract:The spectrum of a random matrix is well-understood for an invariant ensemble, and sufficiently strong information has been obtained for mean field type random matrices. There are however far more general situations where much less information is obtained: when the entries have a heavy-tailed distribution or when the variance profile has a specific structure. In this talk I discuss some recent discoveries in the latter regime. The topics include: a sharp description for the edge of a symmetric random matrix when its tail decays precisely like x^{-4} (the transition regime); a very weak condition for determining spectral outliers for finite rank perturbations of non-Hermitian random matrices with a banded variance profile; the smallest singular value for rectangular random matrix with entries in the domain of attraction of alpha-stable law; and on convergence to the circular law for ESDs of some nonhomogeneous matrices. The work employs recent concentration inequalities invented by Bandeira, Boedihardjo, van Handel and Brailovskaya. While satisfying results are obtained for some problems, a sharp understanding is still not obtained for other problems despite significant quantitative improvement.

Speaker: Søren Galatius (Columbia University)Title: Hopf algebra spectral sequences related to $\textit{K}(\mathbb{Z}$) and the Grothendieck–Teichmüller groupAbstract: The general linear group of the integers acts on the symmetric space $GL_n(\mathbb{R})/O(n)$, and the orbit space $X_n$ can be regarded as a “moduli space of real tori”. The compactly supported cohomology of these spaces forms the $E_1$ page of a spectral sequence converging to the cohomology of $BK(\mathbb{Z})$, the onefold delooping of the algebraic $K$-theory space. I will sketch how to construct a Hopf algebra structure on this spectral sequence, and how it maps to another spectral sequence of Hopf algebras, a version of the Connes–Kreimer Hopf algebra. In recent joint work with Brown, Chan, and Payne (2405.11528), we use this map of Hopf algebras to deduce lower bounds for the compactly supported cohomology of $X_n$ and of $A_n$, the moduli space of principally polarized abelian varieties.

Jesse Schreger (Columbia)

The MIT wrestling club holds practices in the du Pont Wrestling Room on weeknights 5:30-7pm. All levels of experience welcome! Whether you're looking to learn how to grapple or just want to get in a good workout, wrestling practice is a good time to learn technique, get in some live goes, and have fun with a great group of people.Current schedule is: structured practice MTRF, open mats W, and technique sessions 9-10:30am on Saturday. For more information, contact wrestling-officers@mit.edu.

Do you think yoga is only for young, slender, super-flexible people? Think again!Yoga for Every Body with Catherine provides a gentle yoga experience in the Kripalu tradition. It offers a safe introduction for beginners of all ages, shapes, and sizes, as well as an opportunity for more experienced practitioners to share a gentle, mindful practice.Catherine hopes that this will give everyone an opportunity to turn down the “noise” of daily living and tune in to your own body, mind, and spirit.Registration is required on our wellness class website. If you do not already have an account on this website, you'll need to create one. This is fee-based class and open to the entire MIT community.

Join us on Monday evenings for Argentine tango classes with outstanding instructors Fernanda Ghi, Guillermo Merlo and Mia Dalglish (read their bios on the link). Whether you are completely new to tango, or already have some experience, you will find a friendly environment in which to learn new things and improve your technique. You don't have to bring a partner, since the classes involve rotations with all participants.More info on website: https://sites.google.com/site/mittangoclub/products-services/2025-spring-series?authuser=0