报告题目：The slicing problem by Bourgain and the maximal sections of convex bodies

报告人：熊革教授

单位：同济大学

讲座时间：2024年5月1日16:00-17:00

报告地点：数科院206

报告摘要：In this talk, I will first introduce the famous unsolved slicing problem by Bourgain in detail. Then I will address our recent work on the extremal sections of convex bodies. Bounds for the volume of sections of convex bodies which are in the Lp John ellipsoid positions areestablished. Specifically, When the convex bodies are in the LYZ ellipsoid position, we construct a family of Hanner polytopes, which indeed attain the sharp bounds. This talk is based on the joint work with Lu Xin-Bao and Tao Jiang-Yan.

报告人简介：熊革，同济大学长聘教授 ，博士生导师。熊革教授解决了凸体几何中的几个公开问题，包括Lutwak-Yang-Zhang关于锥体积泛函极值问题的2, 3维情形；由截面确定凸体的Baker-Larman问题的2维情形；他与学生最早提出、并解决了Lp静电容量的Minkowski 问题；完全解决了纽约大学G. Zhang教授关于凸体的John 椭球与对偶惯性椭球一致性的问题。熊革教授在国际纯数学的重要期刊JDG, AIM, IUMJ, IMRN, CVPDE, JFA，CAG, Israel Journal of Mathematics, Discrete and Computational Geometry等上发表论文30余篇。部分成果被写入凸体几何的经典教材《Geometric Tomography》和《Convex Bodies: the Brunn-Minkowski theory》中。

主办单位：江苏大学数学科学学院