報(bào)告人: 朱保成 教授

講座日期：2019-06-17

講座時(shí)間：10:10

報(bào)告地點(diǎn)：長(zhǎng)安校區(qū) 數(shù)學(xué)與信息科學(xué)學(xué)院學(xué)術(shù)交流廳

主辦單位：數(shù)學(xué)與信息科學(xué)學(xué)院

講座人簡(jiǎn)介：

朱保成，湖北民族大學(xué)碩士生導(dǎo)師，特聘教授。西南大學(xué)基礎(chǔ)數(shù)學(xué)博士，加拿大“大西洋數(shù)學(xué)研究中心”博士后，湖北省人才計(jì)劃楚天學(xué)者“楚天學(xué)子”，加拿大紐芬蘭紀(jì)念大學(xué)客座教授。主持完成國(guó)家自然科學(xué)基金青年項(xiàng)目1項(xiàng)，主持完成加拿大AARMS博士后項(xiàng)目1項(xiàng)，中央高校業(yè)務(wù)費(fèi)專(zhuān)項(xiàng)基金1項(xiàng)，參與國(guó)家自然科學(xué)基金3項(xiàng)。近5年來(lái)，在 “Adv. Math.”、“Int. Math. Res. Not.”、“Indiana Univ. Math. J.”、“J. Geom. Anal.”、“Proc. Amer. Math. Soc.”以及“中國(guó)科學(xué)”等期刊上發(fā)表20余篇學(xué)術(shù)論文。曾受邀出席2014年世界數(shù)學(xué)家大會(huì)衛(wèi)星會(huì)議 (ICM, 首爾) 并做30分鐘報(bào)告，受邀出席2019年華人世界數(shù)學(xué)家大會(huì)(ICCM, 北京)并做45分鐘報(bào)告。

講座簡(jiǎn)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).