Date/Time : 11 Feb 2026 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Ansgar Jungel, TU Vienna, Austria

Many thermodynamic mixture and biological multicomponent models can be described by cross-diffusion systems. Although the diffusion matrices are generally neither symmetric and nor positive definite, the systems often possess an entropy (or free energy) structure. We aim to “translate” this entropy structure to two-point approximation finite-volume discretizations. The main difficulty is to adapt the nonlinear chain rule to the discrete level.

In this talk, we present two strategies to define a discrete chain rule, assuming either that the entropy is
the sum of individual entropies or that the entropy describes volume-filling models. Both strategies use suitable
mean formulas, based on the mean-value theorem and the convexity of the entropy functional. This leads to convergent and structure-preserving finite-volume schemes that preserve the local flux, total mass, positivity, and dissipate the entropy. Examples include models for segregating populations and Maxwell-Stefan systems for gas mixtures.

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Date/Time : 04 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Asbjørn Nordentoft, University of Copenhagen

To any thin subgroup of a finite co-volume Fuchsian group one can associate a hyperbolic orbifold with geodesic boundary. The projection of the geodesic boundary gives a stratification (or partition) of the set of all thin subgroups. In this talk I will explain how in some cases one can understand the fibers of this stratification. This is related to the problem of lifting closed geodesics ‘simply and separating’. In the case of the modular group this gives a new and geometric perspective on a construction of Duke, Imamoglu and Toth using (minus) continued fractions.

This is joint work in progress with Ser Peow Tan

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Date/Time : 21 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ming Hong Tee, Boston College

Given any Jordan domain U in the Riemann sphere equipped with the hyperbolic metric, one can construct the Epstein surface in hyperbolic 3 space corresponding to it. One important property of the Epstein surface is that its principal curvatures are related to the Schwazian derivative of the uniformization map of U. In this talk, we will exploit this property to relate the bending lamination of a pleated surface with the Schwazian derivative. Furthermore, if U is a domain for a Weil-Peterson curve, we will show that the hyperbolic metric and the quasi-hyperbolic metric are arbitrary closed and the two corresponding Epstein surfaces are arbitrary closed.

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Date/Time : 19 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jasper Lee, University of California, Davis

Mean estimation is perhaps the most fundamental task in statistics, yet there is a divide between the standard theory and practice. The standard theory recommends taking the sample mean, but whose brittleness forces users to apply ad-hoc outlier removal techniques in practice, leading to documented cases of wrong experimental conclusions. On the other hand, theoretical algorithms designed specifically to mitigate such brittleness (e.g. median-of-means and high-dimensional generalizations) have poor empirical performance that they cannot/should not be adopted either.

In this talk, I’ll discuss our efforts to fully resolve the mean estimation problem, achieving (minimax) estimation error that is sharp even in the leading multiplicative constant. I will present a new multivariate mean estimator that has sharp estimation error in any (small) constant dimensions (in preparation), generalizing our previous 1-dimensional mean estimator (FOCS 2021, ICML 2025). I will also discuss a very simple multivariate mean estimator that achieves sharp error guarantees in the “very high-dimensional” regime (ITCS 2022).

The constant-dimensional mean estimator is joint work with Suraj Mathashery, Paul Valiant and Kun Wang, in preparation. The very high-dimensional mean estimator is joint work with Paul Valiant, which appeared in ITCS 2022.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Seog-Jin Kim, Konkuk University, Korea

The square of a graph G, denoted G^2, has the same vertex set as G and has an edge between two vertices if the distance between them in G is at most 2. Thomassen (2018) showed that \chi(G^2)<=7 if G is a subcubic planar graph. A natural question is whether \chi_l(G^2)<=7 or not if G is a subcubic planar graph. Recently Kim and Lian (2024) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim (2025) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph without 4-cycles and 5-cycles. In this talk, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the previous results.

This is joint work with Xiaopan Lian, Atsuhiro Nakamoto, and Kenta Ozeki.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dou Dou, Nanjing University

Ranging from irrational rotations to mixing transformations like horocycle flows, zero entropy systems exhibit very rich and diverse complex structures and dynamical behaviors. In this talk, we will introduce recent developments in the theory of complexity and entropy-type invariants for zero entropy systems, along with our related work on entropy dimensions.

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Date/Time : 14 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Denny Wu , New York University

Modern machine learning systems operate in high-dimensional regimes, with large numbers of data points, features, and parameters. High-dimensional statistical tools, such as random matrix theory, enable sharp, quantitative analyses of tractable model abstractions that nevertheless capture empirical phenomena in modern deep learning. In this talk I will highlight several examples in which such analyses yield precise characterizations of: (i) optimal ridge regularization in the overparameterized regime and the surprising “negative ridge” observation; (ii) how neural networks acquire useful features during the early phase of gradient-based training; and (iii) how emergent risk curves connect to neural scaling laws in SGD learning. Beyond the mathematical insight, I will also discuss the predictive power of these results and the algorithmic implications in more realistic settings.

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Date/Time : 14 Jan 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Li Xiaoli, Shandong University

The magnetization structures in the form of topological solitons have become important research interest following the fabrication of various ferromagnetic materials. In this talk we first present new higher-order implicit-explicit (IMEX) schemes for the LLG equation. These schemes are linear, length preserving, modified energy stable and only require solving one elliptic equation at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates of orders 1 to 5 in a unified framework. Next we present some recent developments in constructing the linear, length preserving and original energy preserving schemes.

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