Upcoming talk:
题目：从Math4AI到AI4Math的初步探索
报告人：罗涛（上海交通大学）
地点：双清C654
时间：10：00-11：00 am，Oct. 16, 2026
腾讯会议：612-884-251
会议密码：123456
摘要：人工智能的蓬勃发展正重塑科学研究范式，数学与AI的深度交叉呈现出“双向赋能”的新格局。本报告将汇报团队近期在“Math4AI”（基于数学理论的深度学习机理解析）与“AI4Math”（基于人工智能的数学研究辅助）两个方向的初步探索。在Math4AI层面，我们引入几何测度论、动力系统与渐近分析方法，深入剖析深度学习的训练动力学机制，针对偏微分方程求解中的泛化失效、神经网络训练中的参数凝聚与秩坍缩现象，以及注意力机制中“聚焦-稀释”的多阶段演化规律提供了初步的理论诠释。在AI4Math层面，我们致力于弥合自然语言与形式语言的语义鸿沟，提出了算子树与结构化自然语言等数学知识表示框架。该框架不仅显著提升了自动形式化的准确率与语义评估的鲁棒性，更为数学文献的智能检索与学生、专家的交互式研读提供了有力工具。报告最后将展望这一交叉领域的未来挑战与研究愿景。
个人介绍：罗涛，上海交通大学数学科学学院/自然科学研究院副教授。2012年获上海交通大学致远学院学士学位，2017年获香港科技大学博士学位，并获香港数学会最佳博士论文奖。2017至2020年，担任普渡大学数学系Golomb访问助理教授。研究方向为计算材料科学、深度学习数学理论（Math4AI）和数学智能（AI4Math）。研究内容包括材料科学的 Peierls–Nabarro 模型、Cauchy–Born 法则；深度学习的频率原则、凝聚理论；数学智能的自动形式化、语义评估、结构化自然语言等。在 ARMA/SIAM 系列/M3AS/JMLR/NeurIPS/ICML/ICLR 等应用数学和机器学习期刊和会议发表论文 40 余篇。获NeurIPS 2025 Oral（top 0.35%）、ICML 2026 Oral（top 0.7%）等。
Past talks:
Date&Time: June 3rd, 2026 9-10 AM Beijing, China
Venue: Zoom Online meeting
Meeting ID: 891 8508 1544
Passcode: YMSC123
Speaker: Ivan Miranda de Almeida (IMPA)
Title: Finite index constant mean curvature hypersurfaces in low dimensions
Abstract: We prove that every complete finite index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in the space forms of positive curvature in dimension six. We also prove that every complete finite index CMC hypersurface immersed in the hyperbolic six-space with $|H|>7$ is compact. These results are closely related to questions posed by M. P. do Carmo, O. Chodosh and H. Hong.
Introduction: Ivan Miranda de Almeida is currently a Ph.D. student at IMPA under the supervision of Prof. Lucas Ambrozio. His research focuses on Geometric Analysis, particularly on the theory of constant mean curvature hypersurfaces.
Date&Time: April 22nd, 2026 9-10 AM Beijing, China
April 21st, 2026 9-10 PM Toronto/US Eastern
Venue: Tecent/Voov meeting
Meeting ID: 205-764-180
Passcode: 123456
https://meeting.tencent.com/dm/tpKsjyYvG38Y
Title: CIC Type-Checking as Growing a Content-Addressed Hypergraph
Speaker: Xinze Li (University of Toronto)
Abstract: Expressions of the Calculus of Inductive Constructions carry a natural directed hypergraph structure in the sense of Barkeshli, Douglas, and Freedman. We show that CIC type-checking is equivalent to growing a content-addressed directed hypergraph, and verify this against a traditional tree-based kernel on 15 declarations from Nat through Nat.add_comm.
Date&Time: Oct 21st, 2025 9-10 AM Beijing, China
Oct 20th, 2025 9-10 PM Toronto/US Eastern
Venue: Online Zoom meeting
Meeting ID: 882 1154 4564 Passcode: YMSC111
Speaker: Isabel Beach (University of Toronto)
Title: The Quantitative Geometry of Geodesics
Abstract: The goal of quantitative geometry is to provide effective versions of known existence theorems for geometric objects. For example, following Serre's proof of the existence of infinitely many geodesics connecting any two points on a closed Riemannian manifold, one may attempt to prove a length bound for these geodesics. In this talk, we will provide a survey of current quantitative theorems concerning geodesics and explore how such results can be proven. In particular, we discuss recent work on the existence of "short" geodesics that meet a given submanifold orthogonally.
Date&Time: June. 27th, 2025, 14:00-15:00
Venue: Jingzhai (静斋) 218
Speaker: Zetian Yan (UC Santa Barbara)
Title: Recent progress on fourth order Willmore energy
Abstract: We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in $R^n$ and establish a connected sum energy reduction for the general fourth-order Willmore energy, analogous to the seminal result of Bauer and Kuwert. We will also discuss recent progress on the study of energy quantization on fourth order Willmore energy.
Date&Time: May. 27th, 2025, 13:30-14:30
Venue: 双清C654
Title: Mass Lower Bounds for asymptotically locally flat 4-manifolds
Speaker:Jian Wang (王健) （中国科学院数学研究所）
Abstract: The mass, a crucial global geometric invariant, intricately relates with
scalar curvature in the different setting. I will explain the relation between asymptotically locally flat (ALF) 4-manifolds and their ADM mass. Specifically, I will talk about how the topology at infinity influences the ADM mass within the ALF setting.
Date&Time: Mar. 12th, 2025, 10:00-11:00 am (Beijing time)
Venue: online zoom meeting: 890 9835 3295 Password: 111111
Speaker: Omar Alshawa (University of Toronto)
Title: Riemannian 3-spheres that are hard to sweep out by short curves
Abstract:
Does every Riemannian 3-sphere M contain a closed geodesic whose length is bounded from above by some function f(d,V) of the diameter d and volume V of M? One strategy to find such a closed geodesic is to construct a sweepout of M by closed curves of length at most f(d,V). In collaboration with Herng Yi Cheng, we prove that this method of finding short closed geodesics does not work for a certain class of sweepouts.
Let L>0 be large. We show that there exists M of diameter and volume less than 1 such that for any sweepout of M by closed curves within this class, one of the curves must be longer than 1.
Date&Time: Jan. 2nd, 2025, 14:00-15:00
Venue: 线上腾讯会议：832-674-246 Password: 111111
Speaker: Jintian Zhu (朱锦天) (Westlake University)
Title: Splitting theorem for Kähler manifolds
Abstract: In this talk, we will establish a Cheeger-Gromoll type splitting theorem for Kähler manifolds with nonnegative mixed curvature based on the conformal method. For our purpose, first we will recall basic knowledge on the Cheeger-Gromoll splitting theorem and Kähler manifolds, and then we will present our theorem and its proof with the conformal method in detail.
Date&Time: Nov. 27, 2024, 10:30-11:30 am
Venue: Online Zoom Meeting ID: 834 6034 2049 Password: 111111
Speaker: Yujie Wu (Stanford University)
Title: The $\mu$-bubble Construction of Capillary Surfaces
Abstract: We introduce a method of constructing (generalized) capillary surfaces via Gromov's "$\mu$-bubble" method. Using this, we study low-dimensional manifolds with nonnegative scalar curvature and strictly mean convex boundary. We prove a fill-in question of Gromov, a band-width estimate, and a compactness conjecture of Martin. Li in the case of surfaces.
Introduction: Yujie Wu is currently a Ph.D. Student at Stanford University advised by Prof. Otis Chodosh. Her research focused on geometric analysis and PDEs, in particular minimal surface theory and the Allen Cahn equation.
