Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Juncheng Wei, The Chinese University of Hong Kong

In 2023, one year before his death, H. Brezis posted 28 open questions which he described as “challenging and difficult”. In this talk I will give complete answer to the first open question—Problem 1.1 on Brezis-Nirenberg problem on three dimensional unit ball, and the seventh open question—Problem 3.1 on harmonic map equation on disk.

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Date/Time : 16 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Svetlana Makarova, Australian National University

When introducing the notion of moduli problems, perhaps the most trivial example one may consider is the “functor of points” of a variety X, whose “classifying space” (moduli space) is X itself. Its very close relative is the stack of ideal sheaves of length 1 subschemes: when X is normal and of dimension at least 2, this stack is the product of X with BG_m. Despite the apparent triviality, modifying this stack gives rise to interesting birational phenomena, about which I will speak. I will describe a certain enlargement U of the stack of ideal sheaves that yields, via taking the good moduli space, a birational contraction of X, and an open substack of U that yields a surgery diagram via non-GIT wall-crossing. If time permits, I will explain how the interpretation of the surgery as a fine moduli of sheaves helps prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero (https://arxiv.org/abs/2508.13395).

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Date/Time : 04 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Sven Leyffer, Argonne National Laboratory

Many design, planning and decision problems arising in engineering, sciences, finance, and statistics can be modeled as mixed-integer nonlinear optimization problems. A challenging class of mixed-integer problems are topology design problem, such as additive manufacturing and the design of cloaking devices. In topology optimization, the physical response of the design is modeled as partial-differential equations (PDEs) and the design is modeled with binary variables defined on each element of the discretization of the PDE. This approach results in mixed integer PDE-constrained optimization (MIPDECO) problem that combine the computational challenges of PDEs with the combinatorial challenges of a massive number of discrete variables. We show that despite their seemingly hopeless complexity, certain MIPDECOs can be solved efficiently (at a cost comparable to a few continuous PDE-constrained optimization solves). We discuss two classes of methods: rounding techniques that are asymptotically optimal, and randomized search techniques. We illustrate these solution techniques with examples from topology optimization.

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Date/Time : 04 Mar 2026 16:30
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Katrin Tent, Universität Münster

The Cherlin-Zilber Conjecture states that an infinite simple group with a notion of dimension that behaves like Zariski dimension should in fact be a linear algebraic group over an algebraically closed field. In this survey I will review what is known and how the Burnside problem comes into the picture.

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Date/Time : 26 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lingrui Ge, Peking University

We develop the dual based approach and introduce several new concepts and tools for the study of one-frequency quasiperiodic operators with analytic potentials. As applications we solve some long-standing arithmetic conjectures: the ten martini problem, sharp phase transition in frequency and absolute continuity of the integrated density of states, for the entire class of type I operators.

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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 : 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 : 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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