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题目：Finite homogeneous metric spaces with special properties

报告人：Yu.G. Nikonorov

Abstract : 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.

时间：2024年 3月22日15:00-16：00

地点：首都师范大学新教二927室

报告人简介：俄罗斯科学院南方数学所教授，研究领域：微分几何、李理论等

联系人：许明