The Tianyuan Summer Seminar on Functional Analysis and Spaces is held annually by the Institute for Advanced Study in Mathematics of HIT. This series of seminars aims to bring together experienced as well as young researchers in the field of functional analysis and (Banach/operator) space theory, and focus on the current mainstream topics in and around this research domain. The seminar provides an ideal platform for young researchers to exchange new ideas and to step forward collaboration.
The 2025 seminar series will continue to focus on mainstream topics in modern functional analysis and related fields. This year’s program will delve into the geometric theory of metric spaces, exploring its interdisciplinary connections with harmonic analysis, probability theory, and computational science. Additionally, the seminar will invite distinguished experts and outstanding young scholars to share cutting-edge advances in the aforementioned areas, as well as in noncommutative Lp-spaces, harmonic analysis, free probability, quantum information, and other theoretical frontiers, fostering collaboration and discussion. This seminar is strongly supported by the Tianyuan Fund for Mathematics of the National Natural Science Foundation of China.
Time: July 21 - August 17, 2025 (with July 20 as arrival day)
Venue: Harbin Institute of Technology
Project leader: Quanhua Xu
Contact: Guixiang Hong (gxhong [AT] hit.edu.cn), Jinghao Huang (jinghao.huang [AT] hit.edu.cn), Simeng Wang (simeng.wang [AT] hit.edu.cn), Xiao Xiong (xxiong [AT] hit.edu.cn),Xumin Wang（xumin.wang【AT】hit.edu.cn)
Registration deadline: June 8, 2025 (Sunday)
Registration link: https://wj.qq.com/s2/22204032/bc12/
(If you have submitted the registration form but do not receive a reponse from us by June 14, please contact us.)
活动安排（将根据研讨班进度更新）
Working group on Analysis and Geometry on Metric Spaces
Abstract: The goal of this seminar is to understand the geometry of Banach spaces using tools from metric geometry and analysis, following the ideas of Ribe’s program. The Ribe program originates from a remarkable rigidity theorem by Martijn Ribe in 1976, which states that uniform homeomorphisms between Banach spaces preserve their local linear structure. This result sparked a fundamental idea: classical local properties of Banach spaces, such as type, cotype, and superreflexivity, should have purely metric characterizations independent of linearity. This surprising result led mathematicians to ask: can we describe Banach space geometry using only distances, without relying on the linear structure? The goal of the Ribe program is to systematically develop such metric descriptions and extend the tools of linear functional analysis to the nonlinear, metric setting. The program consists of five parts:
I. Ribe’s Program and Enflo’s Conjecture
II. Bourgain’s Discretization Theorem, and Metric Embeddings
III. Metric Xp Inequalities and Discrete Riesz Transforms
IV. Noncommutative Xp Inequalities and Applications on Group von Neumann Algebras
V Supplementary Topics
The presentations in the working seminars will be primarily given by volunteer junior participants, directed by the organizers as well as other top experts in the field.
July 21, 14:00-16:00, Activity Center, 活动中心 327
July 23, 14:00-15:30, Zhengxin Building, 正心楼 13
Introduction of the Ribe Program, Enflo Type and Enflo’s Conjecture
Speaker: Li GAO (高力), Wuhan University
July 23, 16:00-17:30, Zhengxin Building, 正心楼 13
July 25, 14:00-17:30, Zhengxin Building, 正心楼 13
Metric cotype
Speakers: Zijie JIANG (蒋子杰), Central South University
Yinghua SUN (孙英华), Xiamen University
Research talks
July 21, 14:00-16:00, Activity Center, 活动中心 327
Lifting properties for C* -algebras
Gilles Pisier, Sorbonne University and Texas A&M University
