Title：John ellipsoid, affine isoperimetric inequality and convex geometry

Speaker：熊  革 （同济大学）

Time：2017年12月8日    下午16:00--17:30

Room：东区管理科研楼   数学科学学院1418室

 

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 $/mathbb R^n$. This ellipsoid is called John ellipsoid (named after mathematician Fritz John), and has many apllications in convex geometry, functional analysis and optimizations. Particularly, that combining the isotropic characterization of John ellipsoid with the celebrated Brascamp-Lieb inequality in real analysis, plays a major role to attack reverse isoperimetric problem. In this talk, we will first briefly survey the discipline of convex geometry. Then, the classical John ellipsoid and its applications to affine isoperimetric inequalities will be addressed. With these background material and basic facts in hand, we will introduce our own work on (reverse) affine isoperimetric inequality, which include several papers already published or submitted recently.