R
Rostislav Grigorchuk
Researcher at Texas A&M University
Publications - 161
Citations - 4970
Rostislav Grigorchuk is an academic researcher from Texas A&M University. The author has contributed to research in topics: Group (mathematics) & Ergodic theory. The author has an hindex of 33, co-authored 157 publications receiving 4676 citations. Previous affiliations of Rostislav Grigorchuk include Steklov Mathematical Institute & Moscow State University.
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Journal ArticleDOI
Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means
TL;DR: In this article, a negative solution to the problem of Milnor concerning the degrees of growth of groups was given, which also answers a question of Day concerning amenable groups and a number of other results are obtained on residually finite finitely generated infinite 2-groups.
Journal ArticleDOI
The Lamplighter Group as a Group Generated by a 2-state Automaton, and its Spectrum*
Rostislav Grigorchuk,A Zuk +1 more
TL;DR: In this article, the lamplighter group is shown to be a 2-state automaton with a spectral measure in [−1,1] and a spectral spectral measure of the spectral measure on a dense countable set of points in [ −1, 1] is computed.
Book ChapterDOI
Just Infinite Branch Groups
TL;DR: The first examples of groups with a branch structure appeared at the end of the 1970s and the beginning of the 1980s ([45] [13] [14], [24] and as discussed by the authors ).
Book ChapterDOI
From fractal groups to fractal sets
Abstract: The idea of self-similarity is one of the most fundamental in the modern mathematics. The notion of “renormalization group”, which plays an essential role in quantum field theory, statistical physics and dynamical systems, is related to it. The notions of fractal and multi-fractal, playing an important role in singular geometry, measure theory and holomorphic dynamics, are also related. Self-similarity also appears in the theory of C*-algebras (for example in the representation theory of the Cuntz algebras) and in many other branches of mathematics. Starting from 1980 the idea of self-similarity entered algebra and began to exert great influence on asymptotic and geometric group theory.