Date/Time : 11 Mar 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nguyen Thi Van Anh, Hanoi National University of Education

The Allen–Cahn equation is a reaction–diffusion equation of mathematical physics which describes the process of phase separation in multi-component alloy systems, including order-disorder transitions. The relation between the approximate Allen–Cahn equations and mean curvature flow has been an ongoing investigation for several decades. For well-prepared initial conditions, Evans, Soner, and Souganidis proved the convergence to the viscosity solutions, Ilmanen showed convergence results to a Brakke flow, and many others. For a general initial conditions, Alfaro, Hilhorst and Matano carried out an analysis showing that the solution develops a steep transition layer within a specific time scale of parameters. In this talk, I will consider the Allen-Cahn equation under the initial condition that is no longer well-prepared and even discontinuous, in particular it is simply as a ‘signed function’ of a given set. The solvability of problems, the convergence to the mean curvature flows in both classical and weak sense are discussed. This is a part of an ongoing research project with Giovanni Bellettini.

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Date/Time : 11 Mar 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Georg Weiss, University of Duisburg-Essen

While global solutions of the obstacle problem have recently been completely characterized (Eberle-Figalli-Weiss 2025), the class of global solutions to the Bernoulli problem is, by a result of M. Traizet (2013), much richer and closely related to minimal surfaces.

In this talk, we explain why a frequency formula of the type used in the obstacle problem is unlikely to be valid for the Bernoulli problem. We also present progress on a different approach—one that does not rely on complex analysis—which appears to be a promising alternative for studying global solutions of the Bernoulli problem.

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Date/Time : 11 Mar 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Zhang Xiaoyan, National University of Singapore

Chaitin’s Omega is defined to be the halting probability of a randomly constructed program. Equivalently it can be defined by the sum of Kolmogorov weights of all binary strings. In this talk we investigate the Omega function f that maps a real x to the sum of Kolmogorov weights of all strings on the left of x. We establish properties of f and compare it with previously defined Omega-related functions. We present that (i) f is strictly increasing, continuous and differentiable precisely at density random reals; (ii) The range of f is a null, nowhere dense, perfect Pi01(0′) class with Hausdorff dimension 1; (iii) there are continuum many x such that f(x) is not random.

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Date/Time : 11 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Sun Song, Zhejiang University

Einstein metrics serve as the counterpart in Riemannian geometry to Einstein spacetimes in general relativity. As one of the most important geometric structures, the study of Einstein metrics is deeply connected to various branches of mathematics, including complex algebraic geometry, low-dimensional topology, partial differential equations, and mathematical physics. In this talk we will discuss recent advances in understanding the construction and classification of Einstein metrics.

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Date/Time : 06 Mar 2026 14:30
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Max Welling, CuspAI & University of Amsterdam

Prof. Dr. Max Welling is a full professor and research chair in machine learning at the University of Amsterdam and a Merkin distinguished visiting professor at Caltech. He is co-founder and CTO of the startup CuspAI – a frontier AI company harnessing AI to unlock materials breakthroughs. He is also a member of the Royal Dutch Academy of Sciences, a fellow at the Canadian Institute for Advanced Research (CIFAR) and the European Lab for Learning and Intelligent Systems (ELLIS) where he served on the founding board. His previous appointments include Partner and VP at Microsoft Research, VP at Qualcomm Technologies, professor at UC Irvine.

Prof. Max Welling finished his PhD in theoretical high energy physics under supervision of Nobel laureate prof. Gerard ‘t Hooft. He then switched fields to focus on machine learning, first as a postdoc at Caltech under supervision of prof. Pietro Perona and then as postdoc under supervision of Nobel laureate prof. Geoffrey Hinton at UCL & U. Toronto.

Prof. Max Welling is a preeminent computer scientist and physicist with over 200,000 Google Scholar citations. His landmark contributions include inventing the Variational Autoencoder (VAE), a foundational architecture in generative AI, and Graph Convolutional Networks (GCNs), which revolutionized the processing of structured data such as molecules and social networks. Furthermore, he pioneered Stochastic Gradient Langevin Dynamics (SGLD) for Bayesian learning and has led the advancement of Equivariant Neural Networks, which integrate fundamental geometric symmetries into deep learning models.

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Date/Time : 06 Mar 2026 13:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ralf Spatzier, University of Michigan

I will discuss ideas in the proof of Margulis’ super rigidity theorem and Zimmer’s cocycle rigidity theorem.

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Date/Time : 04 Mar 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ralf Spatzier, University of Michigan

I will introduce the main ingredients for classifying hyperbolic  higher rank habelian actions.

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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 : 02 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chenji Fu, University of Bonn

Eteve computed the Genestier-Lafforgue L-parameters for depth-zero representation for a equal-characteristic local field. I will explain how to adapt his method to the setting of Fargues-Scholze. We use certain ”smoothness” and ”properness” of the stack of shtuka to reduce the question to the local Hecke stack, where we can do an explicit computation using hyperbolic localizations following the work of ALWY on central sheaves in mixed characteristic.

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