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.

Add to calendar :

Date/Time : 16 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Lo Chi-Heng, National University of Singapore

Local Arthur packets consist of local components of automorphic representations. In the study of automorphic representations, it is often important to understand the properties of a local representation through the local Arthur packets to which it belongs. However, a local representation may lie in multiple local Arthur packets. This causes difficulty, but also provides extra structure for these kinds of problems. In this series of talks, we will discuss the intersection phenomenon for p-adic symplectic and special odd orthogonal groups. We will then explore several applications, including the closure ordering conjecture for local Arthur packets and Jiang’s conjecture on the upper bounds of wavefront sets (and more).

In the first talk, I will introduce the definition of local Arthur packets and their basic properties, and then sketch a geometric construction of local Arthur packets under certain assumptions

Add to calendar :

Date/Time : 12 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 11 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

Add to calendar :

Date/Time : 10 Sep 2025 16:30
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Wang Zhongjian, Nanyang Technological University

In this talk I will discuss the role of regularity estimate for viscous Hamilton Jacobi equation in showing the optimal iteration complexity (square root of dimension) of the Diffusion model. In our approach to the optimal bound, we only assume the Gaussian tail assumption, which does not require log-concaveness of the distribution. Our Gaussian tail assumption admits distribution of early stopping setting and scalable to infinite dimensions. More recently, we also provide analysis for Follmer process and show the deterministic heat flow is a Lipschitz change of variable between target and Gaussian under the Gaussian tail assumption.

Add to calendar :

Date/Time : 10 Sep 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Fanhao Kong, Peking University

We consider a class of weakly asymmetric continuous microscopic growth models with polynomial smoothing mechanisms, general nonlinearities and a Poisson type noise. We show that they converge to the KPZ equation after proper rescaling, where the coupling constant depends on all details of the smoothing and growth mechanisms in the microscopic model. This provides a first example of Hairer-Quastel type with both generic nonlinearity and non-Gaussian noise. This talk is based on the joint work with Haiyi Wang and Weijun Xu.

Add to calendar :

Date/Time : 10 Sep 2025 17:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Frank Stephan, National University of Singapore

Degtev constructed in 1976 recursively enumerable many-one degrees with the following properties: no least one-one degrees inside the many-one degree; one least but no minimal one-one degree inside the many-one degree; for each natural number k one least and above the least k minimal one-one degrees inside the given many-one degree (which, of course, depends on k). He did not provide a recursively enumerable many-one degree with infinitely many minimal one-one degrees and Odifreddi put it in 1981 as an open question into his survey paper. According to Batyrshin, the question was in 2021 still open. This talk will now provide the construction of such a many-one degree with infinitely many minimal one-one degrees. Such a degree has a least one-one degree below them. This is joint work with Sanjay Jain, Linus Richter, Samuel Alfaro Tanuwijaya and Xiaoyan Zhang; a write-up is under preparation.

Add to calendar :

Date/Time : 08 Sep 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dai Wenhan, National University of Singapore

Under categorical local Langlands, certain natural coherent sheaves on Vogan stacks give rise to matching automorphic sheaves on Bun_G, which are generally hard to understand. Understanding the stalks of these automorphic sheaves at points of Bun_G would crucially provide a mechanism for the explicit matching of objects along the categorical local Langlands functor. Despite its importance, the general behavior of these stalks remains largely mysterious. In this talk we will study these sheaves for G=GLn at the Vogan stack of the Steinberg parameter. Some recent conjectures predict that at basic points, these stalks are given by generalized Steinberg representations of inner forms of G, up to degree shifts. After formulating the main conjecture, I will report some progress towards its proof in a special case on the degree-zero component of Bun_G, achieved through combinatorial computations inspired by Hansen. If time permits, I will also present an application of the result to cohomology of local Shimura varieties.

Add to calendar :

Date/Time : 04 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Khoat Than, Hanoi University of Science and Technology

Deep neural networks (DNNs) have driven many of the most significant breakthroughs in artificial intelligence in recent years, fundamentally transforming the way we live and work. Tasks that seemed intractable just a decade ago can now be solved with remarkable accuracy by large-scale DNNs. A central reason for their success lies in their ability to generalize: after learning from a finite training set, DNNs often perform surprisingly well on unseen data. Yet, despite this empirical success, the theoretical foundations of generalization in deep learning remain poorly understood, posing a long-standing challenge.

In this talk, I will provide an overview of recent theoretical advances, many of which, despite their elegance, turn out to yield vacuous or impractical guarantees for modern networks. I will then introduce our new approaches, which establish explicit connections between the local behaviors of a DNN across different regions of the data space, the complexity of the data distribution, and the model’s generalization performance. These results reveal novel structural insights and suggest that such perspectives could bring us closer to resolving one of the most fundamental open problems in deep learning.

Add to calendar :