# overview
My research focuses on Group Theory, Dynamical Systems, Low dimensional Topology, Discrete Mathematics, Abstract Harmonic Analysis, Random Walks, Invariant Means, Bounded Cohomology, and L2-invariants.

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4603 Computer Vision And Multimedia Computation

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
Moscow State University - (Moscow, Russia)

# educationAndTraining[].organization.label
Moscow State University - (Moscow, Russia)

# educationAndTraining[].organization.label
Steklov Mathematical Institute - (Moscow, Russia)

# awardsAndHonors[].label
Association of Former Students University-Level Distinguished Achievement Award, The

# awardsAndHonors[].label
Leroy P Steele Prize Seminal Contribution to Research

# publications[].label
On just-infinite periodic locally soluble groups

# publications[].label
Homomorphic images of Branch groups, and Serre's property (FA)

# publications[].label
Finitely generated subgroups of branch groups and subdirect products of just infinite groups

# publications[].label
A minimality property of certain branch groups

# publications[].label
The rank gradient and the lamplighter group

# publications[].label
On Mealy-Moore coding and images of Markov measures

# publications[].label
Constructions of torsion-free countable, amenable, weakly mixing groups

# publications[].label
On the Gap Conjecture concerning group growth

# publications[].label
Uncountably many 2-generated just-infinite branch pro-2 groups

# publications[].label
Uncountably many 2-generated just-infinite branch pro-2 groups

# publications[].label
On Spectra and Spectral Measures of Schreier and Cayley Graphs

# publications[].label
Some Topics in the Dynamics of Group Actions on Rooted Trees

# publications[].label
Self-Similar Groups and Holomorphic Dynamics: Renormalization, Integrability, and Spectrum

# publications[].label
GROUPS OF INTERMEDIATE GROWTH: AN INTRODUCTION

# publications[].label
On the rigidity of rank gradient in a group of intermediate growth

# publications[].label
Spectra of Schreier graphs of Grigorchuk's group and Schroedinger operators with aperiodic order

# publications[].label
Automatic Logarithm and Associated Measures

# publications[].label
On the Spectrum of Hecke Type Operators related to some Fractal Groups

# publications[].label
MYKOLA M. SEM KO (dedicated to the 65th Birthday)

# publications[].publisher
Luhansk Taras Shevchenko National University

# publications[].label
On spectral properties of the Schreier graphs of the Thompson group $F$

# publications[].label
SPECTRA OF CAYLEY GRAPHS OF THE LAMPLIGHTER GROUP AND RANDOM SCHRODINGER OPERATORS

# publications[].label
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups

# publications[].label
On diagonal actions of branch groups and the corresponding characters

# publications[].label
dedicated to Professor I.Ya. Subbotin on the occasion of his 60-th birthday

# publications[].label
The Spectral Problem, Substitutions and Iterated Monodromy

# publications[].label
On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata

# publications[].label
On the question "Can one hear the shape of a group?" and Hulanicki type theorem for graphs

# publications[].label
Finitely generated subgroups of free groups as formal languages and   their cogrowth

# publications[].label
Combinatorial Group Theory and Applications to Geometry

# publications[].label
Automatic logarithm and associated measures

# publications[].publisher
Luhansk Taras Shevchenko National University

# publications[].label
Integrable and Chaotic Systems Associated with Fractal Groups

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
The profinite completion of certain torsion p-groups

# publications[].label
Laplace and Schrdinger operators without eigenvalues on homogeneous   amenable graphs

# publications[].label
On finitely generated subgroups of a certain periodic group

# publications[].publisher
International Union of Crystallography (IUCr)

# publications[].label
Schreier spectrum of the Hanoi Towers group on three pegs

# publications[].label
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces

# publications[].label
Liftable self-similar groups and scale groups

# publications[].label
Finitely generated subgroups of branch groups and subdirect products of just infinite groups

# publications[].label
Spectral properties of a torsion-free weakly branch group defined by a three state automaton

# publications[].label
The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps

# publications[].label
Subshifts with leading sequences, uniformity of cocycles and spectra of   Schreier graphs

# publications[].label
Invariant random subgroups of the lamplighter group

# publications[].label
FINITELY GENERATED SUBGROUPS OF FREE GROUPS AS FORMAL LANGUAGES AND THEIR COGROWTH

# publications[].publisher
Centre pour la Communication Scientifique Directe (CCSD)

# publications[].label
Irreducibility of unitary group representations and reproducing kernels Hilbert spaces

# publications[].label
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters

# publications[].label
On the condensation property of the Lamplighter groups and groups of intermediate growth

# publications[].label
SCHREIER GRAPHS OF GRIGORCHUK'S GROUP AND A SUBSHIFT ASSOCIATED TO A NONPRIMITIVE SUBSTITUTION

# publications[].label
Groups generated by 3-state automata over a 2-letter alphabet, I

# publications[].label
On a question of Wiegold and torsion images of Coxeter groups

# publications[].label
(): Anatolii Mikhailovich Stepin (obituary)

# publications[].label
On growth of random groups of intermediate growth

# publications[].label
Combinatorics of the subshift associated to Grigorchuk's group

# publications[].label
Finitely generated subgroups of free groups as formal languages and their cogrowth

# publications[].label
On the question Can one hear the shape of a group? and a Hulanicki type theorem for graphs

# publications[].label
Groups of Intermediate Growth: an Introduction for Beginners

# publications[].label
Solved and Unsolved Problems Around One Group

# publications[].label
Directional counting for regular languages

# publications[].label
Asymptotic aspects of Schreier graphs and Hanoi Towers groups

# publications[].label
Special issue devoted to the 60th anniversary of the birth of Igor Volodymyrovych Protasov

# publications[].label
On finitely generated subgroups in certain periodic group

# publications[].label
Schreier spectrum of the Hanoi Towers group on three pegs

# publications[].label
Dynamical Systems and Group Actions Preface

# publications[].label
ON SPECTRAL PROPERTIES OF THE SCHREIER GRAPHS OF THE THOMPSON GROUP F

# publications[].label
Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs

# publications[].label
Ergodic decomposition of group actions on rooted trees

# publications[].label
Integrable and Chaotic Systems Associated with Fractal Groups.

# publications[].label
A DESCRIPTION OF SOLUTIONS OF QUADRATIC EQUATIONS IN HYPERBOLIC GROUPS

# publications[].label
On the condensation property of the Lamplighter groups and groups of Intermediate growth

# publications[].label
REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Qn   AND [1/p]n  , p PRIME

# publications[].label
The spectral problem, substitutions and iterated monodromy

# publications[].label
Universal Groups of Intermediate Growth and Their Invariant Random Subgroups

# publications[].label
On just-infiniteness of locally finite groups and their C*-algebras

# publications[].label
Equivalence of homomorphisms of surface groups to free groups and some properties of 3-dimensional handlebodies

# publications[].label
Self-similarity and branching in group theory

# publications[].label
Finitely generated subgroups of free groups as formal languages and their cogrowth

# publications[].publisher
Centre pour la Communication Scientifique Directe (CCSD)

# publications[].label
On the condensation property of the Lamplighter groups and groups of intermediate growth

# publications[].label
Groups generated by 3-state automata over a 2-letter alphabet. ii

# publications[].label
On spectral properties of the Schreier graphs of the Thompson group $F$

# publications[].label
On Mealy-Moore coding and images of Markov measures

# publications[].label
Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs

# publications[].label
On torsion images of Coxeter groups and question of Wiegold

# publications[].label
Finitely generated subgroups of branch groups and subdirect products of just infinite groups

# publications[].label
On MealyMoore coding and images of Markov measures

# publications[].label
Self-similar groups, algebras and Schur complements

# publications[].label
Special issue dedicated to the 60th birthday of an outstanding Ukrainian mathematician, Professor Leonid A. Kurdachenko

# publications[].label
On the question "Can one hear the shape of a group?" and a Hulanicki type theorem for graphs

# publications[].label
Amenable groups without finitely presented amenable covers

# publications[].label
Laplace and Schrdinger operators without eigenvalues on homogeneous amenable graphs

# publications[].label
SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA

# publications[].label
Amenability and paradoxical decompositions for pseudogroups and for   discrete metric spaces

# publications[].label
On growth of random groups of intermediate growth

# publications[].publisher
European Mathematical Society - EMS - Publishing House

# publications[].label
Joint spectrum and infinite dihedral group

# publications[].label
AMENABILITY AND ERGODIC PROPERTIES OF TOPOLOGICAL GROUPS: FROM BOGOLYUBOV ONWARDS

# editorOf[].label
Topological and Asymptotic Aspects of Group Theory AMS Special Session, Probabilitistic and Asymptotic Aspects of Group Theory, March 26-27, 2004, Athens, Ohio : AMS Special Session, Topological Aspects of Group Theory, October 16-17, 2004, Nashville, Tennessee

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Intermediate Growth and Amenability of Groups

# researcherOn[].awardedBy.label
National Security Agency - (Fort George Meade, Maryland, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# inTheNews[].label
Mathematician Earns Prestigious Humboldt Research Award

# etdChairOf[].label
Carroll, David Matthew (2016-08). Periodic Points in Shifts of Finite Type Over Groups with Connections to Growth. Doctoral Dissertation.

# etdChairOf[].label
Benli, Mustafa G (2013-08). Presentations and Structural Properties of Self-similar Groups and Groups without Free Sub-semigroups. Doctoral Dissertation.

# etdChairOf[].label
Kocak, Dilber (2016-08). Growth of Algebras and Codes. Doctoral Dissertation.

# etdChairOf[].label
Kogan, Roman Leonidovich (2017-12). Measures Induced by Automata and Their Actions. Doctoral Dissertation.

# etdChairOf[].label
Savchuk, Dmytro M. (2009-08). Asymptotic, Algorithmic and Geometric Aspects of Groups Generated by Automata. Doctoral Dissertation.

# etdChairOf[].label
Kogan, Roman Leonidovich (2017-12). Measures Induced by Automata and Their Actions. Doctoral Dissertation.

# etdChairOf[].label
Muntyan, Yevgen (2009-05). Automata groups. Doctoral Dissertation.

# etdChairOf[].label
Bondarenko, Ievgen (2007-12). Groups generated by bounded automata and their schreier graphs. Doctoral Dissertation.