Speaker：Jin Li (Shanghai University)

Time：2024-7-10, 16:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

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.