Andrei Raigorodskii: Colorings of spaces, distance graphs, and Ramsey-type problems

By a distance graph in a metric space I mean, as usual, a graph, whose set of vertices lies in a set X endowed with a metric d and whose set of edges is formed by all pairs of vertices at a certain distance or even at a distance from a prescribed set of positive numbers. Distance graphs are closely related with various aspects of modern Ramsey theory, especially in its geometric part. In my talk, I'll give a survey of various extremal problems concerning distance graphs, space colorings, and Ramsey numbers in some geometric settings.