Date/Time : 25 Feb 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Ralf Spatzier, University of Michigan

Symmetry and extremal properties have played a major role in mathematics for a long time. While I will start to discuss this in the context of some Riemannian geometry, I will emphasize more recent work on dynamical systems. Here symmetry expresses itself in terms of having non-trivially commuting maps or flows, or an action of some group with complicated relations. Case in point are actions of semisimple Lie groups, especially ones of higher rank, e.g. SL(n,R) with n at least 3. This is the so-called Zimmer program. I will discuss some recent highlights.

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Date/Time : 25 Feb 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chengyang Shao, Institut des Hautes Études Scientifiques

This is a mini-course with 3 lectures (1.5 hours each).   The time and venue are:
20 Feb (Friday) 3pm-4:30pm S16-03-06
23 Feb (Monday) 3pm-4:30pm S17-05-11
25 Feb (Wednesday) 3pm-4:30pm S17-05-11

This mini-course equips the audience with essential mathematical tools for the construction of stable and unstable invariant manifolds in hydrodynamical free boundary problems. In particular, it will be shown that the nonlinear instability for a moving capillary water jet follows precisely the Rayleigh-Plateau instability law. Being fully nonlinear and nonlocal in nature, such problems exhibit severe loss of derivatives and cannot be treated by standard methods. Therefore, it has remained largely open. Paradifferential calculus, however, provides a refined framework for analyzing nonlinearities, allowing them to be handled in a manner analogous to linear operators. It yields a unified framework addressing the construction of stable and unstable invariant manifolds for quasilinear PDEs or hydrodynamical free boundary problems.

The course consists of three lectures. The first lecture offers a concise introduction to classical partially hyperbolic dynamical systems and the Lyapunov-Perron method, followed by a review of its extensions to semilinear dispersive PDEs and Eulerian systems with fixed boundaries. The specific difficulties arising in quasilinear and free boundary problems are then discussed. The second lecture provides a brief introduction to the calculus of paradifferential operators, emphasizing its algebraic similarities with classical (pseudo)differential operators. In particular, it will be shown how this calculus applies to the analysis of Dirichlet-Neumann operator in free boundary problems. Finally, the third lecture demonstrates how these tools can be applied to construct stable and unstable invariant manifolds for hydrodynamical free boundary problems, thereby extending the classical Lyapunov-Perron method to this setting.

Some familiarity with the standard theory of hyperbolic PDEs, such as paraproduct decomposition and energy estimates, will be helpful. No prior background in dynamical systems is required.

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Date/Time : 24 Feb 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Jing An, Shanghai Jiaotong University

A classical problem in the study of the long-time behavior of advection–reaction–diffusion equations is to characterize the precise asymptotics of front locations. The strength of the advection term induces pushed-to-pulled front transitions, which can be captured by the so-called weighted Hopf–Cole transform. In this talk, I will revisit existing results on convergence to traveling waves in both the pulled and pushed regimes, and demonstrate how this transformation can be applied to the chemotaxis–FKPP system, an important nonlocal advection–reaction–diffusion model, to obtain refined front asymptotics for a wider range of parameters.

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Date/Time : 23 Feb 2026 16:30
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nils Thuerey, Technical University of Munich

In this talk, I will present recent advances from the area of AI and deep learning for physics simulations. A key focus is the utilization of numerical solvers capable of providing gradient information, i.e. “differentiable simulators”. These solvers seamlessly integrate with deep learning algorithms, presenting numerous advantages in arising from AI-based components in solvers, particularly in the context of flow simulations. However, the regular, first-order quantities like gradients are not necessarily optimal for optimizations and learning tasks. I will outline alternative updates, specifically those arising from modified back propagation paths, and discuss their advantages and disadvantages. In addition, I will give an outlook towards generative modeling for PDEs.

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Date/Time : 19 Feb 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Alessandro Pigati, Bocconi University

In this talk we will introduce a PDE way to construct hypersurfaces which are critical for anisotropic integrands. Namely, we study energy concentration for rescalings of an anisotropic version of Allen-Cahn.

Besides a Gamma-convergence result, we will sketch a proof of the fact that energy of stable critical points (of the rescaled Allen-Cahn) concentrates along an integer rectifiable varifold, a weak notion of hypersurface, using stability (or finite Morse index) to compensate for the lack of monotonicity formulas. As for the latter difficulty, we will mention in passing some recent results towards an anisotropic version of the Michael-Simon inequality, obtained in collaboration with Guido De Philippis (revisiting previous work of Almgren).

Among the technical ingredients, we will see a generalization of Modica’s bound and a diffuse version of the stability inequality for hypersurfaces.

This is joint work with Antonio De Rosa (Bocconi University).

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Date/Time : 12 Feb 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : B. Leimkuhler, University of Edinburgh

Brownian and Langevin dynamics have been mainstay mathematical models in the natural sciences for well over a century. Thermostat methods like Nosé dynamics originated in the 1980s as simplified models to mimic properties of thermal baths in molecular simulation. In this talk I will address the unification of these different approaches, their discretization, and their properties as general purpose tools for large scale computation in the physical sciences, machine learning and statistics.

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Date/Time : 11 Feb 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Lu Yong, Nanjing University

We study the non-relativistic limit of the quadratic and the cubic Klein-Gordon equations. For both the quadratic and the cubic Klein-Gordon equations, we show the validation of Schrodinger approximation up to long time of order $\epsilon^{-1}$ in the non-relativistic limit $\epsilon \to 0$, where $\epsilon$ is proportional to the inverse of the speed of light. We show specific error estimates which coincide with the numerical results.

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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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