Colloquia
UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.
Contacts for the colloquium are Simon Marshall and Dallas Albritton.
Spring 2024
| date | speaker | title | host(s) |
|---|---|---|---|
| Monday Jan 22 at 4pm in B239 | Yingkun Li (Darmstadt Tech U, Germany) | Arithmetic of real-analytic modular forms | Yang |
| Thursday Jan 25 at 4pm in VV911 | Sanjukta Krishnagopal (UCLA/UC Berkeley) | Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes | Smith |
| Jan 26 | Jacob Bedrossian (UCLA) | Lyapunov exponents in stochastic systems | Tran |
| Feb 2 | William Chen | ||
| Feb 9 | (held for town hall) | ||
| Feb 16 | Jack Lutz (Iowa State) | Guo | |
| Feb 23 | |||
| Mar 1 | Per-Gunnar Martinsson (UT-Austin) | TBA | Li |
| Mar 8 | Anton Izosimov (U of Arizona) | Gloria Mari-Beffa | |
| Mar 15 | Peter Humphries (Virginia) | Marshall | |
| Mar 20 | Wanlin Li (Washington U St Louis) | Dymarz, GmMaW | |
| Mar 29 | Spring break | ||
| Apr 5 | Ovidiu Savin (Columbia) | Tran | |
| Apr 12 | Mikayla Kelley (U Chicago Philosophy) | Math And... seminar, title TBA | Ellenberg, Marshall |
| Apr 19 | Yanyan Li (Rutgers) | Tran | |
| Apr 26 | Chris Leininger (Rice) | TBA | Uyanik |
Abstracts
Arithmetic of real-analytic modular forms
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions.
Thursday, January 25. Sanjukta Krinshagopal
Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes
In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application.
First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a graph limit or a graph with infinitely many nodes. I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.
Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some recent results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of multilayer simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, and hate speech in social media.
Friday, January 26. Jacob Bedrossian
Lyapunov exponents in stochastic systems
In this overview talk we discuss several results regarding positive Lyapunov exponents in stochastic systems. First we discuss proving "Lagrangian chaos" in stochastic fluid mechanics, that is, demonstrating a positive Lyapunov exponent for the motion of a particle in the velocity field arising from the stochastic Navier-Stokes equations. We describe how this chaos can be used to deduce qualitatively optimal almost-sure exponential mixing of passive scalars. Next we describe more recently developed methods for obtaining strictly positive lower bounds and some quantitative estimates on the top Lyapunov exponent of weakly-damped stochastic differential equations, such as Lorenz-96 model or Galerkin truncations of the 2d Navier-Stokes equations (called "Eulerian chaos" in fluid mechanics). Further applications of the ideas to the chaotic motion of charged particles in fluctuating magnetic fields and the non-uniqueness of stationary measures for Lorenz 96 in degenerate forcing situations will be discussed if time permits. All of the work except for the charged particles (joint with Chi-Hao Wu) is joint with Alex Blumenthal and Sam Punshon-Smith.