Browsing by Author "Grigorchuk, Rostislav"

Now showing items 1-15 of 15

    • Amenable groups without finitely presented amenable covers 
      Benli, Mustafa Gökhan; Grigorchuk, Rostislav; de la Harpe, Pierre (Bulletin of Mathematical Sciences, 2013)
    • Automata groups 
      Muntyan, Yevgen (2010-01-16)
      This dissertation is devoted to the groups generated by automata. The first part of the dissertation deals with L-presentations for such groups. We describe the sufficient condition for an essentially free automaton group ...
    • Finitely Constrained Groups 
      Penland, Andrew Daniel (2015-08-09)
      This work investigates three aspects of the theory of finitely constrained groups, motivated by questions first asked by Rostislav Grigorchuk when he introduced the subject in 2005. The first topic is Hausdorff dimension ...
    • Generalized Grigorchuk's Overgroups: Growth, Cluster Points, and Associated Rational Maps 
      Samarakoon, Supun Thamara (2021-04-26)
      In this dissertation, we construct and investigate a family of groups, indexed by sequences of three symbols, that generalize the famous Grigorchuk's overgroup. Our work is spitted into three parts: (i) study of growth, ...
    • Groups generated by bounded automata and their schreier graphs 
      Bondarenko, Ievgen (2009-05-15)
      This dissertation is devoted to groups generated by bounded automata and geometric objects related to these groups (limit spaces, Schreier graphs, etc.). It is shown that groups generated by bounded automata are contracting. ...
    • Growth of Algebras and Codes 
      Kocak, Dilber (2016-05-31)
      This dissertation is devoted to the study of the growth of algebras and formal languages. It consists of three parts. The first part is devoted to the growth of finitely presented quadratic algebras. The study of these ...
    • Iterated Monodromy Group of Rational Maps 
      Chao, Qian (2018-05-05)
      We describe the iterated monodromy groups of rational functions of the form ∫c(z) = 1+c/z² , where the parameter c lies in certain components of the parameter plane which are attached to the main cardioid. Such a group is ...
    • Measure Theory of Self-Similar Groups and Digit Tiles 
      Kravchenko, Rostyslav (2011-02-22)
      This dissertation is devoted to the measure theoretical aspects of the theory of automata and groups generated by them. It consists of two main parts. In the first part we study the action of automata on Bernoulli measures. ...
    • Measures Induced by Automata and Their Actions 
      Kogan, Roman Leonidovich (2017-12-14)
      In this thesis we explore the theme of automata, measures on spaces of sequences X^N in a finite alphabet X, and their connections. The notion of a finite-state measure (a measure given by a finite automaton, or equivalently, ...
    • Nonlinear embeddings into Banach spaces 
      Swiecicki, Krzysztof Sebastian (2021-07-14)
      Nonlinear embeddings of Banach spaces has been an active field of research since the mid 20th century with many applications to theoretical computer science (Sparsest Cut problem, Nearest Neighbor Search etc), geometry ...
    • On the Gap Conjecture concerning group growth 
      Grigorchuk, Rostislav (Bulletin of Mathematical Sciences, 2014)
    • On the Spectrum and Density of States of Graphs and Groups 
      Kravaris, Cosmas (2022-04-21)
      We study spectra and spectral measures of the discrete Laplacian and Markov operators on the Cayley graph of a finitely generated group G (and more generally the density of states of discrete periodic operators of finite ...
    • Orbit Equivalence Invariants and Examples 
      Wrobel, Konrad (2021-04-26)
      Orbit equivalence is an equivalence relation on measurable actions of groups that’s been studied since the 1950’s. It has connections to many areas of mathematics including descriptive set theory, percolation theory, ergodic ...
    • Periodic Points in Shifts of Finite Type Over Groups with Connections to Growth 
      Carroll, David Matthew (2016-08-02)
      We develop several tools and techniques for constructing or proving the non-existence of weakly and strongly aperiodic shifts of finite type on groups. Additionally, inspired by the classification of all groups of polynomial ...
    • Presentations and Structural Properties of Self-similar Groups and Groups without Free Sub-semigroups 
      Benli, Mustafa G (2013-07-22)
      This dissertation is devoted to the study of self-similar groups and related topics. It consists of three parts. The first part is devoted to the study of examples of finitely generated amenable groups for which every ...