Date/Time : 20 Aug 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yongnam Lee, Institute for Basic Science

Motivated by DeVleming’s work on moduli of surfaces in P^3 and Chen-Hu-Jiang’s work on moduli of threefolds with volume 2 and geometric genus 4, we study the deformation of pairs of P^3 and hypersurfaces using the classification of Q-Gorenstein degenerations of P^3 with canonical singularities. We prove that if a degenerating threefold has canonical singularities, then the moduli space is smooth at the corresponding pair. Consequently, we find some boundary divisors of the moduli of smooth hypersurfaces. Finally, using the double cover method, we derive some information on the moduli space of threefolds X with canonical singularities with the same volume and geometric genus as a double cover of P^3 branched over a hypersurface. This is joint work with Jungkai Chen and Phin-Sing Soo.

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Date/Time : 13 Aug 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We survey progress from the past five years on the distribution of mass in high-dimensional convex bodies and in probability distributions with convexity properties. The concentration of measure phenomenon has traditionally been studied in highly regular or structured settings, such as spheres, Hamming cubes, Gaussian measures, Markov chains, and martingales. It turns out that convexity assumptions provide an alternative source of regularity in high dimensions with remarkably similar features: Lipschitz functions are highly concentrated, the isoperimetric problem is nearly saturated by half-spaces (up to logarithmic factors), and the central limit theorem is nearly as strong as in the setting of independent random variables. The main developments discussed include the resolution of Bourgain’s slicing problem and the Variance Conjecture, as well as recent progress on the isoperimetric problem for high-dimensional convex bodies. Based on joint work with P. Bizeul and J. Lehec.

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Date/Time : 12 Aug 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Wenfei Liu, Xiamen University

The set V of volumes of stable surfaces, as a subset of positive rational numbers, satisfies the descending chain condition. Equivalently, any nonempty subset of V attains the minimum.

In this talk, I will report a joint work with Jihao Liu, showing that the minimal volume of a stable surface with Picard rank 1 is 1/6351, uniquely realized by a normal rational stable surface previously constructed from P^2 with 4 lines by Valery Alexeev and Wenfei Liu.

In the proof of the minimum, we use various filters to narrow down the possible basket of singularities on such a surface.

The last and very crucial one, the so-called pluricanonical product-dimension filter, was suggested to us by the AI!

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Date/Time : 12 Aug 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Boaz Klartag, Tel Aviv University and Weizmann Institute of Science

We prove there exists a lattice sphere packing in R^n whose density is at least c n^2 / 2^n, where c > 0 is a universal constant. Previously known constructions of sphere packings in R^n had densities of the order of magnitude of n / 2^n, up to logarithmic factors. Our proof utilizes a stochastically evolving ellipsoid that accumulates at least c n^2 lattice points on its boundary, while containing no lattice points in its interior except for the origin.

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Date/Time : 07 Aug 2026 9:30 am to 12:00 pm
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Various speakers,

The workshop will focus on concrete Mathematics teaching cases, especially AI-supported and blended-learning approaches. It will be discussion-led: we will use case studies and focused group discussions to explore particular teaching topics in a practical and efficient way. We warmly welcome colleagues to participate actively in the discussions.

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Date/Time : 04 Aug 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Giovanni Brigati, Institute of Science and Technology, Austria

In this talk, I am proposing a gradient-flow interpretation for a class of non-linear kinetic Fokker—Planck equation (among which the linear case of the Vlasov—Fokker—Planck). The challenge lies in the fact that such dynamics are driven by an interplay of conservative and dissipative effects. Namely, free transport, and diffusion in the velocity variables only. Thus, we rely on the geometry of “kinetic optimal transport”, which is based on Newton’s equations. In this framework, regular curves of measures can be rewritten as solutions to Vlasov’s equations, for a certain force field.

The first main result of the talk is a chain rule for a family of free energy functionals along Vlasov’s equations, which allows us to compute the slope of the energy. Curves of maximal slope correspond to solutions to the non-linear kinetic Fokker—Planck equation. I will then discuss convergence for JKO-like schemes, and further analytical properties of the non-linear kinetic equations, together with a few open questions. My presentation is based on joint works with Guillaume Carlier, Jean Dolbeault, Jan Maas, and Filippo Quattrocchi.

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Date/Time : 29 Jul 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yang Siyao, University of Chicago

High-dimensional probability distributions arise throughout scientific computing, yet their estimation, representation, and evaluation are often hindered by the curse of dimensionality. In this talk, I will present a tensor-train-based framework for learning high-dimensional densities from samples. The method first smooths the empirical distribution to reduce its large variance, compresses the resulting coefficient tensor using efficient tensor-train algorithms, and then applies a deconvolution step to recover a functional density estimator. The proposed method can achieve computational complexity linear in both the dimension and the number of samples. Its performance is demonstrated on several tasks, including high-dimensional Boltzmann distribution estimation and image generation.

I will then discuss an application of this framework to molecular dynamics called TT-Metadynamics. In this method, the growing sum of Gaussian bias potentials generated during metadynamics is periodically compressed into a functional tensor train. This avoids exponential grid storage and prevents the cost of evaluating the bias potential from increasing with simulation time. The method enables free-energy exploration with up to 14 collective variables and performs favorably compared with standard metadynamics in high-dimensional examples.

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Date/Time : 29 Jul 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Zhongkai Tao, Institut des Hautes Études Scientifiques

The fractal uncertainty principle, introduced by Dyatlov and Zahl, has become an important tool in the study of spectral gaps for systems with trapping. It quantifies how a function and its Fourier transform can both concentrate near fractal sets. I will talk about some recent progress in the fractal uncertainty principle and its applications to spectral problems. This talk is partly based on joint works with Aidan Backus, James Leng, Xiaoqi Huang, Christopher Sogge, Zhexing Zhang, Alex Cohen and Zhenhao Li.

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Date/Time : 28 Jul 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Chengyang Shao, Institut des Hautes Études Scientifiques

In this talk, I will present a mathematical proof for the existence of time-periodic oscillating capillary droplet. The major difficulty is that the non-flat underlying geometry makes toric Fourier techniques unavailable, while the quasilinear nature still requires delicate spectral analysis. The analysis starts with paraproduct on compact Lie groups based on invariant Littlewood-Paley decomposition, followed by a toolset of explicit formulas for paradifferential operators. In case of zonal symmetry on the 3-sphere, an effectively computable symbolic calculus is available. It will then be shown how this paradifferential toolset is used to construct time-periodic solution to the spherical capillary water waves equation, giving mathematical justification of Rayleigh’s formula for oscillating capillary droplet. The paradifferential method not only incorporates the underlying geometry and analysis, but also effectively balances the loss of regularity caused by small denominators, allowing a “fixed point” style proof instead of Nash-Moser/KAM iteration. The talk is based on a working paper co-authored with Haocheng Yang.

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