Date/Time : 11 Feb 2026 14:00
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 : 11 Feb 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Joe Kileel, The University of Texas at Austin

Often in data science and scientific computing, high-dimensional data is usefully organized into higher-order arrays. The higher-order arrays, also known as tensors, may then be factorized through appropriate multilinear decompositions. This can achieve data compression and/or reveal important latent information.

In this talk, I will give an introduction to low-rank tensor methods for a general mathematical audience. The subject is at the crossroads of linear algebra, optimization, and some geometry.

A focus will be on ensuring computational efficiency, despite the curse of dimensionality inherent in tensor methods. My talk will showcase applications of tensor methods that I have developed, including (time permitting) in computer vision and robotics; mixture modeling in statistics; and the compression of data streams (arising, e.g., from PDE simulations).

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Date/Time : 11 Feb 2026 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Jing Yifan, Ohio States University

We show that for all integers $2\le s\le t$, any $K_{s,t}$-free subset of $[N]$ with size $\Omega(n^{1-1/s})$ must contain a nontrivial solution to every fixed translation-invariant linear equation in at least five variables. This extends earlier results for Sidon sets due to Conlon-Fox-Sudakov-Zhao and Prendiville to the full family of $K_{s,t}$-free sets.

We also study the corresponding problem in vector spaces over finite fields. In $\mathbb F_q^n$ we obtain stronger quantitative bounds, including polylogarithmic savings, by combining Fourier-analytic transference with polynomial-method input from the arithmetic cycle-removal lemma of Fox-Lov\’asz-Sauermann. Joint work with Cosmin Pohoata and Max Wenqiang Xu.

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Date/Time : 10 Feb 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jean Lasserre, Laboratory for Analysis and Architecture of Systems, CNRS, France

In this talk we propose and describe a hierarchy of semidefinite relaxations that approximate as closely as desired the total variation distance between two given measures $\mu$ and $\nu$, from the sole knowledge of their respective moments. We only assume that both satisfy Carleman’s condition (hence with possibly non-compact support). We obtain a sequence of pseudo-moments that converges to moments of the Hahn-Jordan decomposition of $\mu-\nu$. We then apply this technique to the problem of computing mixtures of Gaussians that minimize the TV-distance to a given measure.

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Date/Time : 06 Feb 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Fang Yijia, National University of Singapore

Euclidean Ramsey theory asks if we can find specific geometric structures in colored space. A refined version of this, known as the canonical Ramsey property, asks: Does every finite coloring of Euclidean space contain a congruent copy of a shape that is either monochromatic or rainbow (all in different colors)?

While this was known for specific shapes, such as acute and right triangles, the question of whether all triangles satisfy this property remained open. In this talk, I will present a solution to this problem posed by Gehér, Sagdeev, and Tóth. We prove that 4-dimensional space is sufficient to guarantee the canonical property for any triangle. The proof uses rotation arguments and a particular configuration that force monochromatic structures.

(Joint work with Gennian Ge, Yang Shu, Qian Xu, Zixiang Xu, and Dilong Yang.)

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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 : 04 Feb 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Ngoc Cuong Nguyen, Kora Advanced Institute of Science & Technology

We study comprehensively local properties of functions in complex Sobolev spaces, introduced by Dinh and Sibony (2006), on a bounded open sub-set of C^n. The main tool is the corresponding functional capacity for the space which is inspired by the global one due to Vigny (2007). An inequality between this capacity and the Bedford-Taylor capacity for plurisubharmonic functions is proved, which is sharp as far as the exponents are concerned. Moreover, it is shown that the functional capacity is a Choquet capacity. The Alexander-Taylor type inequality for the capacity is also proved. This allows us to strengthen the results in the works of Dinh, Marinescu and Vu (2023), Vigny and Vu (2024).

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dano Kim, Seoul National University

The theory of L2 extension theorems is a central topic in several complex variables with numerous applications to complex/algebraic geometry and complex analysis. They are analogous to vanishing theorems in algebraic geometry and often serve as a stronger counterpart of vanishing as exemplified in the proof of Siu’s invariance of plurigenera. In this talk, in the opposite direction, I will discuss how certain ideas from algebraic geometry are crucially used in answering a question raised by Demailly on understanding general L2 extension theorems, via the theory of log canonical pairs. This talk is partly based on joint work with Xu Wang (Trondheim).

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Date/Time : 04 Feb 2026 13:30
Venue : S16 #03-09
Speaker : Minwoo Chae, Pohang University of Science and Technology

In recent years, diffusion-based deep generative models have achieved remarkable success in various applications. In this talk, we present statistical theories for diffusion models within the framework of nonparametric structured density estimation. To address the curse of dimensionality in nonparametric density estimation, we assume that the underlying density function factorizes into several low-dimensional components. Such factorizable densities are common in important examples, such as Bayesian networks and Markov random fields. We prove that an implicit density estimator constructed from diffusion models achieves the minimax optimal convergence rate with respect to total variation. Technically, we design a novel network architecture, which includes convolutional neural networks as a special case, to construct a minimax optimal estimator.

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