Copolar sets of pseudo-cones

：李晋（上海大学）
：2024-07-10 16:00
：海韵园数理大楼686会议室

报告人：李晋（上海大学）

时  间：2024年7月10日16:00

地  点：海韵园数理大楼686会议室

内容摘要:

In this talk, I will present some properties of pseudo-cones and copolar sets and prove that copolarity is essentially the only abstract duality on pseudo-cones. It is analogue to polarity on convex bodies; see Gruber [Abh. Math. Sem. Univ. Hamburg 1992], Bo ̈r ̈oczky and Schneider [Geom. Funct. Anal 2008] and Schneider [Beitra ̈ge Algebra Geom. 2008]. Our result may also be understood as a counterpart of the characterization of Legendre transforms and A-transforms of convex functions; see Artstein-Avidan and Milman [AIMS Announcements 2007; Ann. of Math. 2009; J. Eur. Math. Soc. 2011] and Cheng and Luo [Sci. China Math. 2021; J. Math. Anal. Appl. 2022]. However, we do not need to assume a lattice duality is bijective to characterize copolarity. The talk is based on joint work with Gangsong Leng and Yun. 

个人简介：

李晋，上海大学副教授。上海大学博士毕业，维也纳工大（Vienna University of Technology）博后。入选上海市高层次青年人才计划、奥地利Lise Meitner博士后计划（2019-2021）。获维也纳工大数学教职工最佳论文奖（2017年度）。在国际著名期刊Adv. Math.、Trans. Amer. Math. Soc.、J. Funct. Anal.、Int. Math. Res. Not.、Indiana Univ. Math. J.等发表多篇学术论文。

 

联系人：程庆进