Speaker：Deping Ye (Memorial University of Newfoundland)

Time：2026-10-19, 10-20, 10-21 15: 00

Location：Conference Room S102 & S205 at Experiment Building at Haiyun Campus

Abstract:

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.