Seminar List | UCI Mathematics

Week of October 19, 2025

Mon Oct 20, 2025
4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics Xue Feng - (UCLA) Learn to Evolve: Unsupervised Neural JKO Operator for Wasserstein Gradient Flow The Jordan–Kinderlehrer–Otto (JKO) scheme is a powerful framework for iteratively solving Wasserstein gradient flows (WGFs), but each JKO subproblem is often computationally expensive. We propose a neural JKO solution operator that efficiently solves WGFs for a family of parameterized energy functionals. A key challenge is that training data typically consists of only one—or a few—initial densities, rather than full trajectories. To address this, we introduce Learn-to-Evolve, an unsupervised algorithm that jointly learns the JKO operator and the trajectory data. The neural network being trained serves as an on-the-fly dynamic data generator: we alternate between generating trajectories with the current model and updating the operator with the newly produced data. This evolving dataset acts as natural data augmentation and improves generalization to unseen energies and initial conditions. This talk will present empirical accuracy and generalization across diverse benchmarks, together with convergence guarantees for the learning framework. I’ll also sketch extensions beyond the JKO setting to other iterative operators and close with an open discussion.

Tue Oct 21, 2025
1:00pm to 2:00pm - RH 340N - Dynamical Systems Karl Zieber - (UCI) Products of Random Matrices and Anderson Localization Abstract: Furstenberg’s theorem for random matrix products has been a key tool in many contexts, including mathematical physics. Of particular interest is the 1-dimensional Anderson model of electron diffusion in random media. In this talk, we will discuss how to apply a version of Furstenberg’s theorem where matrices which are independent but not necessarily identically distributed (non-stationary). In particular, we will discuss how to prove spectral and dynamical localization in the non-stationary Anderson model with unbounded potentials using this version of Furstenberg’s theorem.
3:00pm to 3:50pm - RH 306 - Analysis Zeljko Cuckovic - (University of Toledo) Invertibility of Toeplitz operators on the Bergman space Characterizing invertibility of a Toeplitz operator Tφ on the Bergman space in terms of the properties of the symbol φ has been a long standing open problem. Partial answers can be given by assuming the positivity of the symbol. In this talk we introduce a novel geometric condition on the image of the symbol φ, which relaxes the standard positivity condition. We will also discuss the related Douglas’ problem. (Joint work with Jari Taskinen)
3:00pm - RH 440R - Logic Set Theory Julian Eshkol - (UCI) Bounding the Ultrafilter Number at Successors For an infinite cardinal κ, the ultrafilter number u_κ is the smallest size of a family that generates a uniform ultrafilter on κ. We say that u_κ is bounded if u_κ<2^κ. The case κ=ω is well understood, with the consistency of a bounded ultrafilter number at ω first noted in the early 1970s by Kunen. The method used in Kunen’s construction does not generalize to the case κ=ω_1, and Kunen asked whether u_{ω_1}<2^{ω_1} is even consistent; this remains wide open. The consistency of u_κ<2^κ for general uncountable κ has been studied extensively in the last decade. In this series of talks, we will survey some recent progress towards bounding the ultrafilter number at successor values of κ, with emphasis on a key theorem of Raghavan and Shelah. We will also discuss some crucial limitations to applying this theorem for a bounded ultrafilter number at any of the ω_n’s.
4:00pm to 5:00pm - 306 Rowland Hall - Differential Geometry Jonathan Zhu - (University of Washington) Capillary minimal surfaces in spherical caps Minimal surfaces in the round 3-sphere enjoy a number of attractive and influential rigidity properties, particularly in low genus. Progress has been made in extending these results to certain analogous settings, such as free boundary minimal surfaces in the Euclidean ball. We will propose perspectives by which these other settings may be studied within a continuous family starting with the round 3-sphere. In this talk, we’ll discuss (half-space) intersection properties, connections with capillary minimal surfaces and other free boundary problems. This is based on joint work (including some in progress) with Keaton Naff.

Thu Oct 23, 2025
9:00am to 9:50am - Zoom - Inverse Problems Lauri Oksanen - (University of Helsinki) Minkowski metric is rigid in the Lorentzian Calderón problem https://sites.uci.edu/inverse/
1:00pm to 1:50pm - RH 340N - Algebra Manny Reyes - (UC Irvine) Learning seminar: Hopf algebras and tensor categories A continuation of our introduction to tensor categories of representations. We will define Hopf algebras and explain how their module categories carry a monoidal structure, generalizing the case of representations of a group.
4:00pm - RH 306 - Colloquium Nicolas Monod - (EPFL, Switzerland) Taking big steps and going nowhere: how to moonwalk back from infinity I will tell a story around a theorem we proved with Tom Hutchcroft and Omer Tamuz. In one version of the story, we look for fixed-point theorems in the spirit of Markov-Kakutani but for several maps at the same time. In the other version, we cross out items from a finite list and we ask: is there a random list that would almost not change at all when we cross out any of the first few items? We solve these questions, which are really only one question, by performing what looks like a backwards random walk in which every step would be infinitely long, but stationary.