Date/Time : 25 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Bjoern Bringmann, Princeton University

There has been much recent progress on the local solution theory for geometric singular SPDEs. However, the global theory is still largely open. In this talk, we discuss the global well-posedness of the stochastic Abelian-Higgs model in two dimension, which is a geometric singular SPDE arising from gauge theory. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects, which are controlled using covariant heat kernel estimates. Second, we control nonlinear remainders using a covariant monotonicity formula, which is inspired by earlier work of Hamilton.

This is joint work with S. Cao.

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Date/Time : 25 Nov 2025 10:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Lo Chi-Heng , National University of Singapore

In this talk, I will discuss Jiang’s Conjecture, which predicts an upper bound for the wavefront set of any representation of Arthur type in terms of the local Arthur packet containing it. I will then describe its generalization to ABV-packets and to arbitrary irreducible representations (not necessarily of Arthur type), and show that all these formulations of Jiang’s Conjecture are in fact equivalent. Moreover, I will explain that these conjectures can be further reduced to the case of anti-tempered representations.

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Date/Time : 24 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Leonardo Nagami Coregliano, The University of Chicago

The classic de Finetti’s Theorem from 1931 says that an infinite sequence of random variables is invariant under permutations (exchangeable) if and only if it is a mixture of i.i.d. random variables. For a long time, this was considered a curiosity of classic probability theory. In the 80s, exchangeability was revived with the Aldous–Hoover Theorem which completely characterized exchangeable distributions of random matrices (i.e., distributions invariant under simultaneous permutations of rows and columns), and more generally tensors. Since the resulting Aldous–Hoover representation theorem yielded complicated representations, Hoover asked which distributions admitted simpler representations, called $\ell$-independent representations and noticed that a natural assumption, called $\ell$-locality, was necessary but not sufficient.

In this talk, I will cover surprising connections of exchangeability theory with combinatorics and learning theory. In the former connection, exchangeability can be used to construct semantic/geometric limits of dense combinatorial objects, which capture the asymptotic behavior of densities of subobjects; in turn, these limit objects are used to study quasirandomness and connect back to Hoover’s question on independence vs. locality. In the latter connection, exchangeability forms the backbone of high-arity probability approximately correct (PAC) learning theory, which is a natural learning theory for learning hypergraphs. In turn, high-arity PAC learning theory can be used to obtain better bounds in tame hypergraph regularity lemmas, which connect back to Aldous–Hoover representations of low rank (a notion dual to $\ell$-independence).

No background in exchangeability theory, limit theory or learning theory is required to follow the talk.  This talk is based on several joint works with Maryanthe Malliaris, Alexander Razborov, Caroline Terry and Henry Towsner.

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Date/Time : 24 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Wang, Chao, Southern University of Science and Technology

Variational Bayesian inference offers a powerful framework for tackling key challenges in tensor analysis and image restoration, which are critical problems in machine learning and computer vision. This talk presents innovative approaches to address these challenges by integrating Bayesian principles, variational inference, and physical modeling. First, we introduce a Bayesian framework for Tensor Robust Principal Component Analysis (TRPCA) to recover low-rank structures and characterize sparse noise in mixed-noise scenarios. By embedding a low-rank tensor nuclear norm prior and a generalized sparsity-inducing prior within a Bayesian framework, our method learns the optimal tensor nuclear norm and balances low-rank and sparse components automatically. Second, we propose a novel physics-informed optimization framework for jointly solving depth estimation and image restoration from a single defocused image. By modeling the defocused image as a function of a depth map and an all-in-focus (AiF) image based on optical physics, the framework leverages their intrinsic connections. The depth map guides AiF image recovery, while the AiF image regularizes the depth map reconstruction via reconstruction error. A variational inference algorithm, parameterized with deep neural networks, ensures flexibility and high performance.

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Date/Time : 21 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 21 Nov 2025 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Matthew Shunshi Zhang, University of Toronto

We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure π \propto exp(−V). Borrowing techniques from Malliavin calculus, we compute estimates for the Radon-Nikodym derivative for processes which may anticipate the Brownian motion, in the sense that they may not be adapted to the filtration at the same time. Applying these to various popular midpoint discretizations, we are able to improve the regularity and cross-regularity results in the literature on sampling methods. We also obtain a query complexity bound of O(d^{1/4}) for obtaining a ε^2-accurate sample in 𝖪𝖫 divergence, under log-concavity and strong smoothness assumptions for ∇^2 V.

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Date/Time : 20 Nov 2025 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lénaïc Chizat, École Polytechnique Fédérale de Lausanne (EPFL)

Recent progress in AI has been fueled by training neural networks of ever-increasing size, a difficult craft guided largely by heuristics. A promising approach to provide principled foundations for this discipline is to analyze neural networks via their infinite-size limits. While the large-width limit is now relatively well understood and has already yielded practical tools adopted in industry (such as μP), the extension of the theory to large-depth models has remained elusive.

In this talk, I will present the first analysis that rigorously captures the joint infinite-width and infinite-depth limit for architectures used in practice. Our approach combines techniques from stochastic approximation, propagation of chaos and dynamical mean-field theory. The resulting framework provides phase diagrams, quantitative error bounds, and conceptual insights. For instance, our theory shows that models of infinite depth, regardless of their actual width, behave throughout training as though they were also infinitely wide. Overall, our analysis sheds new light on the structure of training dynamics and suggests a path toward principled methods for scaling deep neural networks.

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Date/Time : 20 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yang Daodao, Eastern Institute of Technology, Ningbo

The metric theory of Diophantine approximation investigates whether typical real numbers can be well approximated by rational numbers. In 1924, Khintchine proposed the first 0-1 law in metric Diophantine approximation: assuming that the approximation function has a certain monotonicity, this law provides a necessary and sufficient condition for typical real numbers to be well approximated by infinitely many rational numbers. In 1941, Duffin and Schaeffer attempted to generalize Khintchine’s theorem without assuming that the approximation function has monotonicity. Their proposed new 0-1 law, known as the Duffin–Schaeffer conjecture, became a central problem in Diophantine approximation. After considerable efforts by many number theorists, the Duffin–Schaeffer conjecture was finally resolved by Koukoulopoulos and Maynard in 2019. A remaining challenge is to establish a quantitative law, similar to the strengthening of Khintchine’s theorem by Erdős and Schmidt, to estimate the number of reduced fractions that can approximate the given real number sufficiently well. In 2022, Aistleitner, Borda and Hauke established a quantitative version of the Duffin–Schaeffer conjecture, but the error term they obtained only achieved a logarithmic power-saving. An open problem is to establish an asymptotic formula with a power-saving error term. In a recent joint work with Koukoulopoulos and Maynard, we prove a quantitative version of the Duffin–Schaeffer conjecture with an almost sharp error term.

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Date/Time : 19 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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