Наредни састанак Семинара биће одржан онлајн у четвртак 3.марта 2022. са почетком у 17.15 преко Webex платформе.
Предавач: Yu. G. Nikonorov, Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
Наслов предавања: ON FINITE HOMOGENEOUS METRIC SPACES
Апстракт:
A metric space (M,d) is called homogeneous if for every points x,y in M, there is a self-isometry f of the space (M,d) such that f(x)=y.
A metric space (M,d) is called generalized normal homogeneous if for every points x,y in M, there is a self-isometry f of the space (M,d) such that f(x)=y and d(x,f(x)) >= d(z,f(z)) for any z in M.
A metric space (M,d) is called Clifford-Wolf homogeneous if for every points x,y in M, there is a self-isometry f of the space (M,d) such that f(x)=y and d(x,f(x))= d(z,f(z)) for any z in M.
In this talk, we are going to discuss mainly finite metric spaces with various degrees of homogeneity. Partial cases of finite homogeneous metric spaces are the vertex sets of compact convex (including regular and semiregular) polytopes in Euclidean spaces, whose isometry groups acts transitively on the set of vertices.
In recent papers, we obtained the classifications of generalized normal homogeneous and Clifford~Wolf homogeneous metric spaces that are sets of vertices of regular or semiregular polytopes in Euclidean spaces (with the induced metric). The main part of the talk is devoted to the presentation of these classifications.
This talk is based on recent papers written in collaboration with Professor V. N.Berestovskii (Sobolev Institute of Mathematics, Novosibirsk).
Линк за приступ:
https://matf.webex.com/matf/j.php?MTID=m59be71caf48dc02dcf1a94eb5b56755b
Meeting number (access code): 2409 188 6780
Meeting password: PpsJV3kEX32.