BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yurii G. Nikonorov (Southern Mathematical Institute of the Vladika vkaz Scientific Center of the Russian Academy of Sciences) DTSTART:20230322T160000Z DTEND:20230322T170000Z DTSTAMP:20260423T052837Z UID:VSGS/67 DESCRIPTION:Title: Fi nite homogeneous metric spaces with special properties\nby Yurii G. Ni konorov (Southern Mathematical Institute of the Vladikavkaz Scientific Cen ter of the Russian Academy of Sciences) as part of Virtual seminar on geom etry with symmetries\n\n\nAbstract\nThis talk is devoted to some recent re sults on finite homogeneous metric spaces obtained in joint papers with Pr of. V.N. Berestovskii. Every finite homogeneous metric subspace of an Eucl idean space represents the vertex set of a compact convex polytope with th e isometry group that is transitive on the set of vertices\, moreover\, al l these vertices lie on some sphere. Consequently\, the study of such subs ets is closely related to the theory of convex polytopes in Euclidean spac es.\n\nThe 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 homogenei ty property.\nThe normal homogeneity and the Clifford - Wolf homogeneity d escribe more stronger properties than the homogeneity. Therefore\, it is q uite natural to check the presence of these properties for the vertex sets of regular and semiregular polytopes.\n\nIn 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 classific ation of polyhedra with all edges of equal length and with 2-point homogen eous vertex sets.\n\nThe most recent results and still unsolved problems i n this topic will also be discussed.\n LOCATION:https://researchseminars.org/talk/VSGS/67/ END:VEVENT END:VCALENDAR