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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Date/Time : 04 Feb 2026 15:00
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Zhang Pingwen, Wuhan University and Peking University

Real numbers underpin mathematical research and the understanding of natural phenomena. The real number set comprises rational numbers (a measure-zero set) and irrational numbers (a full-measure set), implying that systems governed by irrational numbers are more prevalent. However, current computers cannot exactly store or represent irrational numbers, rendering numerical computations for irrational-dominated systems susceptible to Diophantine errors—incurred when approximating irrationals with rationals. Such errors significantly compromise numerical results. In this talk, we analyze the mechanism of Diophantine error and its impact on numerical computations. We also develop an approximation theory for multi-dimensional quasiperiodic functions with Diophantine frequencies when approximated by periodic functions. To avoid Diophantine errors, we propose two novel algorithms: the projection method and the finite points recovery method, which extend high-precision numerical computation from the rational to the real domain. Leveraging the ergodic and arithmetic properties of irrational numbers, we establish the mathematical foundations of these algorithms. Furthermore, we present their applications to several irrational-dominated scientific problems to discover new physical phenomena, including quasicrystals and their phase transitions, interfacial structures in materials, and quasiperiodic Schrödinger operators.

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Gunter Schuetz, University of Lisbon

The symmetric Dyson exclusion process (SDEP) is a stochastic interacting particle system with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric simple exclusion process and as a discrete version of Dyson’s Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. This allows for proving an explicit formula for the time evolution of the expected microscopic particle density. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling and non-local hydrodynamics where the current is a genuinely non-local functional of the density given by a Hilbert transform. This non-local one-field description is equivalent to a local complex Burgers equation for finite particle density. Closed evolution formulas allow us to solve the melting of single and double block initial states, producing limit shapes and arctic curves that agree with large-scale Monte Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.

(joint work with J. Dubail and A. Zahra)

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