Date/Time : 19 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.

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Date/Time : 18 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.

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Date/Time : 17 Sep 2025 17:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Andrea Volpi, University of Udine

This is joint work with Damir Dzhafarov and Reed Solomon. A relational structure is strongly indivisible if for every partition M = X0 ⊔ X1, the induced substructure on X0 or X1 is isomorphic to M. Cameron (1997) showed that a graph is strongly indivisible if and only if it is the complete graph, the completely disconnected graph, or the random graph. We analyze the strength of Cameron’s theorem using tools from computability theory and reverse mathematics. We show that Cameron’s theorem is is effective up to computable presentation, and give a partial result towards showing that the full theorem holds in the ω-model REC. We also establish that Cameron’s original proof makes essential use of the stronger induction scheme IΣ2.

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Date/Time : 17 Sep 2025 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Li Yifei, University of Tübingen

In this talk, we present a numerical analysis of the Eyles-King-Styles tumour growth model, a free boundary problem with nontrivial bulk-surface coupling. Unlike existing evolving bulk problems or evolving surface problems, this bulk-surface coupling necessitates H^{1/2}-order analysis on the surface Γ. We establish a comprehensive H^{1/2}(Γ) framework that captures the coupling between the bulk and surface. It enables a rigorous convergence analysis for continuous finite elements of polynomial degree at least 3, yielding optimal-order H^1(Ω)/H^{1/2}(Γ) error bounds.

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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 : 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

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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.

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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.

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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.

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