讲座内容简介：

The dual Brunn-Minkowski theory, initiated by Lutwak, provides powerful tools to solve the long-standing Busemann-Petty problem in the 1990's. Among those deep results, the dual Brunn-Minkowski and dual Minkowski inequalities are the most important.

In this talk, I will discuss the newly introduced dual Orlicz-Brunn-Minkowski theory, a nontrivial extension of the dual Brunn-Minkowski theory. In particular, I will talk about the dual Orlicz-Minkowski and dual Orlicz-Brunn-Minkowski inequalities. These inequalities are based on the Orlicz-addition of star bodies, and are thought to be the heart of the dual Orlicz-Brunn-Minkowski Theory. Finally, I will mention the Orlicz intersection bodies and the Orlicz-Busemann-Petty problem (an unsolved problem).

讲座人简介：

朱保成，湖北民族大学硕士生导师，特聘教授。西南大学基础数学博士，加拿大“大西洋数学研究中心”博士后，湖北省人才计划楚天学者“楚天学子”，加拿大纽芬兰纪念大学客座教授。主持完成国家自然科学基金青年项目1项，主持完成加拿大AARMS博士后项目1项，中央高校业务费专项基金1项，参与国家自然科学基金3项。近5年来，在 “Adv. Math.”、“Int. Math. Res. Not.”、“Indiana Univ. Math. J.”、“J. Geom. Anal.”、“Proc. Amer. Math. Soc.”以及“中国科学”等期刊上发表20余篇学术论文。曾受邀出席2014年世界数学家大会卫星会议 (ICM, 首尔) 并做30分钟报告，受邀出席2019年华人世界数学家大会(ICCM, 北京)并做45分钟报告。