Date/Time : 07 Aug 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Zijian Wang, Nankai University and NUS

In this talk, we will present several new results investigating the (in)stability properties of rotating drops and jets. 

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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 : 05 Aug 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Thorsten Schmidt, University of Freiburg

Affine and polynomial processes have been one of the most important class in mathematical finance due to their tractability and flexibility. However, the analysis was mostly limited to the classical Markov-process theory which focuses on stochastically continuous processes. In this work, we take the more general viewpoint and start from a finite-dimensional semimartingale and analyse the properties of affine and polynomial processes. This has important applications in many fields, in particular in the overnight interest rate markets.

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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 : 04 Aug 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Timo Sprekeler, Texas A&M University

In this talk, we discuss a computational multiscale method for the mixed formulation of Darcy’s problem, based on a stable localized orthogonal decomposition in Raviart-Thomas finite element spaces. In the spirit of numerical homogenization, the construction provides low-dimensional coarse approximation spaces that incorporate fine-scale information from the heterogeneous coefficients by solving local patch problems on a fine mesh. The resulting numerical scheme is applicable beyond periodicity and scale-separation. This is joint work with Patrick Henning (Bochum) and Hao Li (Hong Kong).

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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 : 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 : 28 Jul 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Zhongkai Tao, Institut des Hautes Études Scientifiques

The initial data of the vacuum Einstein equations on a spacelike hypersurface satisfy the Einstein constraint equations. It is an underdetermined PDE system. We exploit the underdeterminedness to find nontrivial solutions of the Einstein constraint equations with interesting properties. A key ingredient is the construction of Bogovskii-type operators for underdetermined PDEs satisfying a robust symbol condition. The Bogovskii-type operators have favorable support and regularizing properties, allowing us to manipulate the solutions flexibly. This is based on joint work (partly in progress) with Philip Isett (Caltech), Yuchen Mao (UC Berkeley), and Sung-Jin Oh (UC Berkeley)

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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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