Rostislav Grigorchuk | Academic Influence

Rostislav Grigorchuk's AcademicInfluence.com Rankings

Rostislav Grigorchuk

Mathematics

#1817

World Rank

#2903

Historical Rank

Group Theory

#21

World Rank

#29

Historical Rank

Algebra

#156

World Rank

#244

Historical Rank

Number Theory

#295

World Rank

#369

Historical Rank

mathematics Degrees

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Mathematics

Rostislav Grigorchuk's Degrees

PhD Mathematics Taras Shevchenko National University of Kyiv
Masters Mathematics Taras Shevchenko National University of Kyiv
Bachelors Mathematics Taras Shevchenko National University of Kyiv

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Why Is Rostislav Grigorchuk Influential?

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According to Wikipedia, Rostislav Ivanovich Grigorchuk is a mathematician working in different areas of mathematics including group theory, dynamical systems, geometry and computer science. He holds the rank of Distinguished Professor in the Mathematics Department of Texas A&M University. Grigorchuk is particularly well known for having constructed, in a 1984 paper, the first example of a finitely generated group of intermediate growth, thus answering an important problem posed by John Milnor in 1968. This group is now known as the Grigorchuk group and it is one of the important objects studied in geometric group theory, particularly in the study of branch groups, automaton groups and iterated monodromy groups. Grigorchuk is one of the pioneers of asymptotic group theory as well as of the theory of dynamically defined groups. He introduced the notion of branch groups and developed the foundations of the related theory. Grigorchuk, together with his collaborators and students, initiated the theory of groups generated by finite Mealy type automata, interpreted them as groups of fractal type, developed the theory of groups acting on rooted trees, and found numerous applications of these groups in various fields of mathematics including functional analysis, topology, spectral graph theory, dynamical systems and ergodic theory.

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Rostislav Grigorchuk's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means (1985) (606)
Bernside's problem on periodic groups (1980) (323)
The Lamplighter Group as a Group Generated by a 2-state Automaton, and its Spectrum (2001) (241)
From fractal groups to fractal sets (2002) (203)
On a Torsion-Free Weakly Branch Group Defined by a Three State Automaton (2002) (158)
On problems related to growth, entropy, and spectrum in group theory (1997) (152)
On the Spectrum of Hecke Type Operators related to some Fractal Groups (1999) (151)
Solved and Unsolved Problems Around One Group (2005) (146)
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces (2016) (124)
On Parabolic Subgroups and Hecke Algebras of Some Fractal Groups (1999) (104)
On a question of Atiyah (2000) (96)
Asymptotic aspects of Schreier graphs and Hanoi Towers groups (2006) (94)
Topological and Asymptotic Aspects of Group Theory (2006) (88)
Some topics in the dynamics of group actions on rooted trees (2011) (77)
Milnor's Problem on the Growth of Groups and its Consequences (2011) (67)
On the asymptotic spectrum of random walks on infinite families of graphs (1997) (66)
Lie Methods in Growth of Groups and Groups of Finite Width (2000) (63)
ON THE HILBERT-POINCARÉ SERIES OF GRADED ALGEBRAS ASSOCIATED WITH GROUPS (1990) (60)
Groups St Andrews 2005: Self-similarity and branching in group theory (2007) (60)
Groups of Intermediate Growth, an Introduction (2008) (50)
Schreier spectrum of the Hanoi Towers group on three pegs (2007) (48)
Spectral properties of a torsion-free weakly branch group defined by a three state automaton (2002) (48)
ON THE GROWTH DEGREES OF $ p$-GROUPS AND TORSION-FREE GROUPS (1986) (47)
Classification of groups generated by 3-state automata over a 2-letter alphabet (2008) (45)
Complete growth functions of hyperbolic groups (1997) (43)
Groups St Andrews 1997 in Bath, I: On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata (1999) (39)
Пример конечно определенной аменабельной группы, не принадлежащей классу $EG$@@@An example of a finitely presented amenable group not belonging to the class $EG$ (1998) (37)
Self-similar groups, operator algebras and Schur complement (2007) (36)
of Group Actions on Rooted Trees (2016) (36)
Spectra of Schreier graphs of Grigorchuk’s group and Schroedinger operators with aperiodic order (2014) (31)
Invariant random subgroups of lamplighter groups (2015) (30)
On the lattice of subgroups of the lamplighter group (2012) (29)
Irreducibility of unitary group representations and reproducing kernels Hilbert spaces (2003) (29)
On a conjecture of Atiyah (2000) (28)
Amenable actions of nonamenable groups (2007) (27)
Amenability and ergodic properties of topological groups: from Bogolyubov onwards (2014) (25)
Cancellative semigroups of power growth (1988) (25)
The Spectral Problem, Substitutions and Iterated Monodromy (2007) (25)
Groups of Intermediate Growth: an Introduction for Beginners (2006) (24)
The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees (2003) (24)
On spectra of Koopman, groupoid and quasi-regular representations (2015) (24)
Ergodic properties of boundary actions and the Nielsen–Schreier theory (2009) (24)
On the Gap Conjecture concerning group growth (2012) (22)
Self-similar groups acting essentially freely on the boundary of the binary rooted tree (2012) (22)
Invariant random subgroups of the lamplighter group (2012) (21)
Just-infinite C*-algebras (2016) (21)
Ergodic theorems for actions of free groups and free semigroups (1999) (20)
Amenable groups without finitely presented amenable covers (2012) (20)
Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive substitution (2015) (20)
Groups generated by 3-state automata over a 2-letter alphabet. II (2006) (19)
One-Relator Groups of Exponential Growth Have Uniformly Exponential Growth (2001) (18)
Эргодические теоремы для действий свободной группы и свободной полугруппы@@@Ergodic theorems for the actions of a free group and a free semigroup (1999) (18)
A Description of solutions of quadratic equations in hyperbolic Groups (1992) (18)
From Self-Similar Groups to Self-Similar Sets and Spectra (2015) (18)
An Example of an Indexed Language of Intermediate Growth (1999) (17)
Universal groups of intermediate growth and their invariant random subgroups (2015) (17)
ON THE PROBLEM OF THE EXISTENCE OF AN INVARIANT MEAN ON A GROUP (2017) (17)
Characteristic random subgroups of geometric groups and free abelian groups of infinite rank (2014) (16)
The Group of Automorphisms of A 3-Generated 2-Group of Intermediate Growth (2004) (16)
Spectra of non-commutative dynamical systems and graphs related to fractal groups (2000) (16)
Superamenability and the problem of occurrence of free semigroups (1987) (15)
The profinite completion of certain torsion p-groups (2000) (15)
Diameters, distortion, and eigenvalues (2010) (13)
Growth functions, rewriting systems, and the Euler characteristic (1995) (12)
Construction ofP-groups of intermediate growth that have a continuum of quotient groups-groups of intermediate growth that have a continuum of quotient groups (1984) (12)
On a problem of day on nonelementary amenable groups in the class of finitely defined groups (1996) (11)
On just-infiniteness of locally finite groups and their $$C^*$$C∗-algebras (2016) (11)
Invariant measures on homogeneous spaces (1979) (11)
On Dehn Functions of Infinite Presentations of Groups (2009) (11)
On diagonal actions of branch groups and the corresponding characters (2014) (10)
On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups (2015) (10)
The spectral measure of the Markov operator related to 3-generated 2-group of intermediate growth and its Jacobi parameters (2012) (8)
Constructions of torsion-free countable, amenable, weakly mixing groups (2014) (8)
Self-similar groups, automatic sequences, and unitriangular representations (2014) (8)
ON THE TOPOLOGICAL AND METRIC TYPES OF SURFACES REGULARLY COVERING A CLOSED SURFACE (1990) (8)
A group of intermediate growth acting by homomorphisms on the real line (1993) (8)
Ограниченные когомологии групповых конструкций@@@Bounded cohomology of group constructions (1996) (8)
Ergodic decomposition of group actions on rooted trees (2014) (7)
On the question “Can one hear the shape of a group?” and a Hulanicki type theorem for graphs (2018) (7)
On a group associated to $z^2-1$ (2002) (6)
HOMOMORPHIC IMAGES OF BRANCH GROUPS, AND SERRE'S PROPERTY (FA). (2007) (6)
Ветвящиеся группы@@@Branch groups (2000) (5)
Spectra of Cayley graphs of the lamplighter group and random Schrödinger operators (2019) (5)
On a question of Wiegold and torsion images of Coxeter groups (2010) (5)
On just infinite periodic locally soluble groups (2016) (5)
The rank gradient and the lamplighter group (2011) (5)
Topological full groups are locally embeddable into finite groups (2011) (5)
Self-Similar Groups and Holomorphic Dynamics: Renormalization, Integrability, and Spectrum (2020) (5)
О проблеме М. Дэя об неэлементарных аменабельных группах в классе конечно-определенных групп@@@On a problem of day on nonelementary amenable groups in the class of finitely defined groups (1996) (5)
D ec 2 00 6 Groups generated by 3-state automata over a 2-letter alphabet (2008) (4)
Groups: A minimality property of certain branch groups (2004) (4)
On spectra and spectral measures of Schreier and Cayley graphs (2020) (4)
Geometry and Cohomology in Group Theory: On Tychonoff Groups (1998) (4)
Width of elements in free groups (1991) (4)
Classification of epimorphisms of fundamental groups of surfaces onto free groups (1990) (4)
Subshifts with leading sequences, uniformity of cocycles and spectra of Schreier graphs (2019) (4)
Dynamical Systems and Group Actions (2012) (3)
Integrable and Chaotic Systems Associated with Fractal Groups (2020) (3)
On the condensation property of the Lamplighter groups and groups of Intermediate growth (2014) (3)
Combinatorics of the subshift associated with Grigorchuk’s group (2017) (3)
Весовые функции на группах и критерии аменабельности алгебр Берлинга@@@Weight functions on groups and an amenability criterion for Beurling algebras (1996) (3)
Gibbs States on Countable Groups (1985) (3)
On Simple Finitely Generated Amenable Groups (2011) (2)
Анатолий Михайлович Степин (к шестидесятилетию со дня рождения)@@@Anatolii Mikhailovich Stepin (on his 60th birthday) (2001) (2)
Key agreement based on automaton groups (2019) (2)
Weight functions on groups and an amenability criterion for Beurling algebras (1996) (2)
Группы с одним определяющим соотношением экспоненциального роста обладают равномерно экспоненциальным ростом@@@One-Relator Groups of Exponential Growth Have Uniformly Exponential Growth (2001) (2)
On subgroup structure of a 3-generated 2-group of intermediate growth (2008) (2)
Universal Groups of Intermediate Growth (2015) (2)
On torsion images of Coxeter groups and question of Wiegold (2009) (2)
On growth of random groups of intermediate growth (2013) (2)
Uncountably many 2-generated just-infinite branch pro-2 groups (2015) (1)
Presentations of Topological Full Groups by Generators and Relations (2015) (1)
Automatic logarithm and associated measures (2018) (1)
Laplace and Schr\"odinger operators without eigenvalues on homogeneous amenable graphs (2021) (1)
Self-similar groups, algebras and Schur complements (2006) (1)
On spectra of representations and graphs. Erratum (2020) (1)
On Mealy–Moore coding and images of Markov measures (2021) (1)
Finitely generated subgroups of free groups as formal languages and their cogrowth (2021) (1)
Universal groups of intermediate growth and their invariant random subgroups (2015) (1)
Ефиму Исааковичу Зельманову 60 лет (2016) (0)
Конечно порожденные подгруппы ветвящихся групп и подпрямые произведения минимально бесконечных групп (2021) (0)
Дмитрий Викторович Аносов (некролог)@@@Dmitrii Viktorovich Anosov (obituary) (2015) (0)
AMENABILITY AND PARADOXICAL DECOMPOSITIONSFOR PSEUDOGROUPS AND FOR DISCRETE METRIC SPACESTullio (1997) (0)
Can one hear the shape of a group (2019) (0)
Book Review: Self-similar groups (2007) (0)
On the growth of the wallpaper groups. (2020) (0)
Группа асинхронных автоматов и рациональные гомеоморфизмы множества Кантора@@@The group of asynchronous automata and rational homeomorphisms of the Cantor set (2000) (0)
Connection between automatic sequences and endomorphisms of rooted trees via d-adic dynamics. (2019) (0)
Amenable groups without finitely presented amenable extensions (2012) (0)
Efim Isaakovich Zelmanov is 60 years old (2016) (0)
Se p 20 00 On a conjecture of Atiyah (2000) (0)
Book Review: Discrete harmonic analysis (2019) (0)
Solenoid Maps, Automatic Sequences, Van Der Put Series, and Mealy-Moore Automata (2020) (0)
On irreducibility of Koopman and quasi-regular representations of weakly branch groups (2015) (0)
On spectral properties of the Schreier graphs of the Thompson group $F$ (2021) (0)
Book Review: Subgroup growth (2003) (0)
Письмо в редакцию@@@Letter to the editor (1996) (0)
On finitely generated subgroups of a certain periodic group (2002) (0)
Ju l 2 00 2 From Fractal Groups to Fractal Sets (2008) (0)
SOLENOIDAL MAPS, AUTOMATIC SEQUENCES, VAN DER PUT SERIES, AND MEALY AUTOMATA (2022) (0)
On the Rigidity of Rank Gradient in a Group of Intermediate Growth (2018) (0)
Анатолий Михайлович Степин (некролог) (2022) (0)
On spectra of Cayley graphs of the lamplighter group and their spectral measures (2019) (0)

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