地点：行健楼学术活动室665
邀请人：陈慧斌 副教授
摘要：This talk is devoted to some recent results on finite homogeneous metric spaces obtained in joint papers with Prof. V.N. Berestovskii. Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spaces by whether or not their vertex sets have the normal homogeneity property or the Clifford-Wolf homogeneity property. These two properties both are stronger than the homogeneity. Hence, it is quite natural to check these properties for the vertex sets of regular and semiregular polytopes. In the second part of the talk, we consider the m-point homogeneity property and the point homogeneity degree for finite metric spaces. Among main results, there is a classification of polyhedra with all edges of equal length and with 2-point homogeneous vertex sets. The most recent results and still unsolved problems in this topic will also be discussed.
作者简介：Yurii Nikonorov Dr. Sci., Professor (Full) ,Principal investigator, Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences (Vladikavkaz, Russia) .
Graduate of Mechanics and Mathematics Faculty of Novosibirsk State University (1993). Candidate’s dissertation (1995) is devoted to the study asymptotics of mean value points in integral mean value theorems, doctoral dissertation (2004) is devoted to the application of analytical methods in the theory of homogeneous Einstein manifolds. Research interests include Riemannian geometry, Einstein manifolds, geometry of convex bodies, Lie groups and algebras, integral mean value theorems. He is the author of more than 100 scientific papers, including 4 monographs. Four of his students received a Candidate of Science (PhD) degree.
