Title: Geometry of Gromov-Hausdorff distance; classical and modern results
Speaker: Alexey A. Tuzhilin（Moscow State University, Moscow, Russia）
Time: 10:30-11:30, November9
Location: Room 201, Ming De Building
Abstract: We discuss the famous Gromov-Hausdorff distance that measures the best possible matching for each pair of metric spaces: the better matching, the lower distance (for isometric metric spaces the distance vanishes). This distance was applied in various branches of mathematics, from investigation of the groups growth rate, to images recognition. We start our talk from the main necessary definitions and the basic classical facts, and continue with some recent results, in particular, the ones obtained by the author, his colleagues and his students from Moscow State University. We mention some unexpected applications of this distance: to investigation of the classical Borsuk problem on partition of a bounded subset of the Euclidean space into the ones of smaller diameters; to calculation of the clique covering number of a graph; to closely related with the previous one the chromatic number of a graph; and to calculation of the edges lengths of an arbitrary minimum spanning tree. All these results can be found in arxiv.
