Date/Time : 10 Apr 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Samuel Hon, National University of Singapore

The closures of conjugacy classes in classical real linear lie groups were determined by Djokovic in his 1982 paper. Through a series of theorems, the proof reduces to mainly combinatorial arguments which aren’t difficult, but tedious to check. In this talk, I will discuss how we are formalizing the proof in LEAN and how this makes the checks simpler. I will begin with a short introduction on the proof, how and why LEAN works, and how we can leverage AI to simplify and speed up the process.

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Date/Time : 14 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Denny Wu , New York University

Modern machine learning systems operate in high-dimensional regimes, with large numbers of data points, features, and parameters. High-dimensional statistical tools, such as random matrix theory, enable sharp, quantitative analyses of tractable model abstractions that nevertheless capture empirical phenomena in modern deep learning. In this talk I will highlight several examples in which such analyses yield precise characterizations of: (i) optimal ridge regularization in the overparameterized regime and the surprising “negative ridge” observation; (ii) how neural networks acquire useful features during the early phase of gradient-based training; and (iii) how emergent risk curves connect to neural scaling laws in SGD learning. Beyond the mathematical insight, I will also discuss the predictive power of these results and the algorithmic implications in more realistic settings.

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Date/Time : 12 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wang Zhihan, Cornell University

Singularities arise naturally in geometric variational problems and evolution equations. A fundamental question is to understand the local structure of these singular sets, both in general settings and under generic assumptions. In this talk, I will discuss recent progress on the analysis of singularities for the area functional, focusing on structural results and generic regularity phenomena in minimal surfaces and mean curvature flow.

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Date/Time : 01 Dec 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wenkui Du, Massachusetts Institute of Technology

In this talk, I will discuss the singularity theory of mean curvature flow. As the most natural evolution equation in extrinsic geometry, mean curvature flow has striking applications in geometry, topology and image processing. A central challenge for these applications is understanding the structure of singularities. This talk surveys recent progress on the classification of singularity models of mean curvature flow and their applications. In particular, ancient noncollapsed solutions naturally arise when we consider blow-up limits near singularities. Several results about classification of ancient noncollapsed solutions will be presented. I will also mention my future plan of singularity analysis in geometric variational problems. The talk is based on my joint works with collaborators B. Choi, Daskalopoulos, Haslhofer, Šešum, Zhao and Zhu.

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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 : 19 Nov 2025 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Siqing Zhang, Yale University

The Hodge Theorem reveals a fundamental phenomenon in algebraic geometry: the de Rham cohomology can often be identified with the Dolbeault cohomology. The Non Abelian version of this phenomenon “identifies” the moduli of flat connections with the moduli of Higgs bundles. The arithmetic version of this phenomenon echoes these identifications in prime characteristics. In this talk, I will introduce recent advances on the interplay among the Non Abelian Hodge Theories in different characteristics. By bringing moduli theory into the prime characteristic version, we reveal new structures over the complex numbers.

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Date/Time : 17 Sep 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Luo Tao, Shanghai Jiao Tong University

Artificial Intelligence for Mathematics (AI4Math) is a rapidly advancing field with significant implications for both academic research and industrial applications. In this talk, we will review the evolution of AI-driven mathematical reasoning, tracing the transition from intuitive, natural language-based approaches to the rigorous, verifiable proofs enabled by formal languages. After providing a foundational overview, we conduct a technical survey of three key research frontiers within the formal systems: Automated Theorem Proving, Autoformalization, and Automated Semantic Evaluation. The primary focus is placed on our contributions to the latter two areas, which are crucial for bridging the gap between human mathematical knowledge and machine-verifiable logic.

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Date/Time : 25 Jun 2025 10:00
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : François Loeser, Sorbonne University

We will provide a general overview of our work with E. Hrushovski on tame geometry over valued fields, using the stable completion of algebraic varieties over valued fields. A key result is the existence of retractions to piecewise-linear objects called skeleta, which are definably isomorphic to definable subsets of the value group. We will conclude by presenting a recent finiteness result obtained with A. Ducros, E. Hrushovski and J. Ye for tropical functions on such skeleta.

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Date/Time : 25 Apr 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Xu Tianyi, Peking University (BICMR)

This talk explores the latest developments and emerging trends in the application of AI to mathematics, focusing on leveraging generative models for writing formalized mathematical proofs. We will introduce the idea of formalizing mathematics using proof assistants—computer programs designed to verify the correctness of mathematical proofs. We will then compare various approaches to formalization, highlighting the unique advantages of using large language models (LLMs) for this task. Additionally, we will address key challenges that naturally arise in this process and present our strategies for overcoming them.

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