报告人：罗思捷（中南大学）

时  间：7月12日下午14:30

地  点：厦大海韵园实验楼108报告厅

内容摘要:

Functional inequalities such as Poincare inequality, Talagrand inequality, Buser inequality, concentration inequalities, etc., have played an essential role in analysis and probability theory for quite a long time. Surprisingly, their vector-valued extensions have recently been evidenced as crucial tools in studying the nonlinear geometry of Banach spaces. In 2020, a breakthrough was made by Ivanisvili, van Handel, and Volberg, establishing the equivalences of Enflo type and Rademacher type in Banach spaces, settling a long-standing open problem. One of the novel ideas of their approach is the vector-valued Poincare inequality. Since then, numerous functional inequalities have been successfully extended to the vector-valued setting, serving as powerful tools in Banach space theory.

In this talk, we will first recall the fundament work of Ivanisvili et al. and some necessary background of the heat semigroup on hypercubes. Secondly, we will characterize the Rademacher type in terms of Buser inequality, McDiarmid inequality, etc., for functions taking values in Banach spaces via the heat semigroup method. Finally, we will conclude this talk with some applications to random matrices. This talk is based on joint work with Prof. Lixin Cheng and Dr. Wuyi He.

个人简介：

罗思捷，中南大学数学与统计学院讲师，2018年博士毕业于厦门大学，2021年清华大学丘成桐数学科学中心博士后出站。主要研究兴趣为 Banach 空间理论、凸分析、测度集中现象。迄今为止在 Science China Mathematics、Journal of Convex Analysis 等国际期刊发表数篇论文。

联系人：张文