Speaker：Ge Xiong（Tongji University）

Time：2022-07-25, 15:00

Location：Tencent Meeting ID：430-872-422（No Password）

Abstract:

It is known that there exists a unique ellipsoid of maximal volume inside a convex body (a compact convex set with non-empty interiors) in R^n. This ellipsoid is called John ellipsoid (named after mathematician Fritz John), and has many applications in convex geometry, functional analysis, and optimizations. In 2005, E. Lutwak, D. Yang and G. Zhang defined the L_p John ellipsoids for p＞0 and established their associated affine isoperimetric inequalities within the L_p Brunn-Minkowski theory.

In this talk, I will introduce our recent work on L_p John ellipsoids for p＜0. This talk is based on the joint work with Xinbao Lu.