报告人：叶德平（加拿大纽芬兰纪念大学）

时 间：2026年10月19日、10月20日、10月21日15:00

地 点：海韵园实验楼S102（10月19日）、海韵园实验楼S205（10月20日、10月21日）

内容摘要:

Functional inequalities, particularly Sobolev-type inequalities, play a fundamental role in analysis, partial differential equations, and information theory. Many of these inequalities are closely connected to classical geometric inequalities, as illustrated by the relationship between the Sobolev and isoperimetric inequalities. In these two lectures, we will introduce several fundamental results in convex geometry, including the Brunn-Minkowski and Prékopa–Leindler inequalities, and explore their connections with functional inequalities. Particular attention will be given to the geometric approach of constructing convex bodies from functions and deriving functional inequalities from geometric principles. Through concrete examples, we will illustrate the main ideas and techniques underlying this approach. The lectures aim to provide an accessible introduction to the interplay between convex geometry and functional analysis.  

个人简介：

叶德平，加拿大Memorial University终身教授。主持加拿大国家自然科学基金(NSERC) 项目。现任加拿大数学会旗舰杂志Canadian Journal of Mathematics、Canadian Mathematical Bulletin以及加拿大数学会新杂志Canadian Mathematical Communications的副主编(Associate Editor)，并于2017年获得JMAA Ames奖。长期从事凸几何分析、几何和泛函不等式、随机矩阵、量子信息理论和统计学等领域的研究。已在 Comm. Pure Appl. Math., Adv. Math., J. Funct. Anal., Math. Ann., CVPDE等国际著名杂志（数学类，数学物理类和统计类）上发表论文40多篇。

联系人：程庆进