- AMSS-YMSC-BIMSA拓扑及应用进展联合讨论班

Depth in arrangements: Dehn--Sommerville--Euler relations with applications

组织者

段海豹 , Fei Han , Yong Lin , 潘建中 , 魏国卫 , 吴杰 , 夏克林 , 丘成栋 , Chao Zhou

演讲者

Herbert Edelsbrunner

时间

2022年05月26日 16:00 至 17:00

地点

1110

线上

Zoom 361 038 6975 (BIMSA)

摘要

The depth of a cell in an arrangement of $n$ (non-vertical) great-spheres in $S^d$ is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn--Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements. This is work with Ranita Biswas, Sebastiano Cultrera, and Morteza Saghafian.

演讲者介绍

Herbert Edelsbrunner is one of pioneers for topological and geometric approaches to data science, by his excellent research on the topic during the decades, from his PhD thesis on computational geometry in 1982 and assistant professorship in Information Processing at the Graz University of Technology during 1981-1985, to his professorship positions at UIUC, Duke and ISTA. Professor Edelsbrunner received Alan T. Waterman Award, he is members of the Academia Europaea, the American Academy of Arts and Sciences and the German Academy of Sciences Leopoldina. Professor Edelsbrunner is widely recognized as one of founding fathers of the new-born area of topological data analysis (TDA).