Rostislav Ivanovich Grigorchuk (Russian: Ростислав Иванович Григорчук; Ukrainian: Ростисла́в Iва́нович Григорчу́к; b. February 23, 1953) is a mathematician working in different areas of mathematics including group theory, dynamical systems, geometry and computer science.
Grigorchuk is particularly well known for having constructed, in a 1984 paper,[1] the first example of a finitely generated group of intermediate growth, thus answering an important problem posed by John Milnor in 1968.
He obtained a PhD (Candidate of Science) in Mathematics in 1978, also from Moscow State University, where his thesis advisor was Anatoly M. Stepin.
[21] Rostislav Grigorchuk gave an invited address at the 1990 International Congress of Mathematicians in Kyoto[22] an AMS Invited Address at the March 2004 meeting of the American Mathematical Society in Athens, Ohio[23] and a plenary talk at the 2004 Winter Meeting of the Canadian Mathematical Society.
[1] This result answered a long-standing open problem posed by John Milnor in 1968 about the existence of finitely generated groups of intermediate growth.
These are finitely generated groups of automorphisms of rooted trees that are given by particularly nice recursive descriptions and that have remarkable self-similar properties.
The study of branch, automata and self-similar groups has been particularly active in the 1990s and 2000s and a number of unexpected connections with other areas of mathematics have been discovered there, including dynamical systems, differential geometry, Galois theory, ergodic theory, random walks, fractals, Hecke algebras, bounded cohomology, functional analysis, and others.
Important connections have been discovered between the algebraic structure of self-similar groups and the dynamical properties of the polynomials in question, including encoding their Julia sets.