Recording: https://disk.pku.edu.cn:443/link/BC2A84C65A65A46B5303EFAE1C4212AA
Valid Until: 2026-06-30 23:59
Abstract: Let $(X, \rho)$ be a finite metric space. Consider the space of real functions on $X$ with zero mean. Equip it with Lipschitz norm $\|f(x)\|=\max |f(x)-f(y)|/\rho(x, y)$ and consider the unit ball in this norm, which is a certain convex polytope. The question on classifying metrics depending on the combinatorics of this polytope have been posed by Vershik in 2015. In a joint work with J. Gordon (2017), we proved that for generic metric space the number of faces of a given dimension is always the same. This fact is intimately related to regular triangulations of the root polytope (convex hull of the roots of root system $A_n$). In this survey-style talk, we discuss both this phenomenon and further relations of the subject, observed recently by several groups of mathematicians.
Bio: Prof. Fedor Petrov is an expert in Combinatorics, Convex Geometry, Functional Analysis and Geometry of Numbers. Being a former student of Prof. A.M. Vershik, now he plays a leading role in his research group. Prof. Petrov graduated from Saint Petersburg State University in 2004, got his PhD in 2007 and habilitation (Doctor of Sciences degree) in 2018. He is a Professor and a director of one of the educational programs at the Department of Mathematics and Computer Sciences of Saint Petersburg State University combining this with a research position at the Saint Petersburg Department of Steklov Mathematical Institute. Not only Prof. Petrov is an author of a big number of impressive results in the aforementioned areas, but also a jury member of several top mathematical contests for high school and university students. Besides, he is a member of the Council of the St. Petersburg Mathematical Society (since 2018).
