Some Recent Papers
Submitted

On justinfinite periodic locally soluble groups, with P.Shumyatsky (arxiv)

Justinfinite C*algebras, with Magdalena Musat, Mikael Rordam (arxiv)
 On diagonal actions of branch groups and the
corresponding characters, with A.Dudko, (arxiv).
Published/Accepted

Joint spectrum and infinite dihedral group, with R.Yang,
Proceedings of the Steklov Institute of Math.
(to appear) (56 pages) (arxiv)
 On justinfiniteness of locally finite groups and their C*algebras,
with V.Belyaev, P.Shumyatsky, Bull. Math. Sci., avaiable online, (arxiv)
 Characteristic random subgroups of geometric groups and
free abelian groups of infinite rank , with L.Bowen and R.Kravchenko ,
Trans. Amer. Math. Soc. v.369 (2017), no. 2 ,
755–781. (arxiv).
 On spectra of Koopman, groupoid and quasiregular representations, with Artem Dudko. Journal of Modern Dynamics,
v.11,
2017,
99123 (arxiv)
 On
irreducibility and disjointness of Koopman and quasiregular representations of weakly
branch groups, with A Dudko.
Accepted
at Contemporary Math. The volume dedicated to the memory of D.V. Anosov.
 Universal Groups of Intermediate Growth and their
invariant random subgroups, with Mustafa Gokhan Benli, Tatiana Nagnibeda, Funk. Anal. And Priloz. (Functional Analysis and its applications) 49,
no.3, 159174 (arxiv).
 Lamplighter groups, de Bruijn
graphs, spiderweb graphs and their spectra, with PaulHenry Leemann, Tatiana Nagnibeda, Journal
of Physics A.
J. Phys. A 49 (2016),
no. 20, 205004, 35 pp (arxiv).
 Ergodic decomposition of group actions on rooted trees,
with D.Savchuk, Proceedings of the Steklov
Institute of Math. (2016), vol. 292, pp. 94111) (arxiv).
 Spectra of Schreier graphs of
Grigorchuk's group and Schroedinger
operators with aperiodic order, with D.Lenz and T.SmirnovaNagnibeda , (arxiv).
 Selfsimilar groups, automatic sequences, and unitriangular representations, with Y.Leonov, V.Nekrashevych and
V.Sushchansky , Bull. Math. Sci. (2016), 6, no. 2, 231–285 (arxiv).
 Constructions of torsionfree countable, amenable,
weakly mixing groups, with R.Kravchenko and A.Olshanskii , L'Enseignement
Mathematique Enseign. Math. (2015),
61, 321—342 (arxiv).
 Amenability and ergodic properties of topological
groups: from Bogolyubov onwards, with P. de la Harpe, LMS Lecture Notes (to appear)
, (arxiv).

From selfsimilar groups to selfsimilar sets and spectra,
with V.Nekrashevych, Z.Sunic, Fractal Geometry and Stochastics V, Progress in Probability,
70 (2015),
pp. 175207.
 On growth of random groups of intermediate growth with M. Benli and Y. Vorobets Groups,
Geometry, and Dynamics, 8, (2014), no. 3, 643667 , (arxiv)
 Selfsimilar groups acting essentially freely on the
boundary of the binary rooted tree with D. Savchuk, In: Group Theory,
Combinatorics, and Computing. Contemp. Math. v.611, Amer. Math. Soc. 2014,
948. (arxiv)
 Invariant random subgroups of the lamplighter group,
with L.Bowen, R.Kravchenko,
Israel J. Math. 207 (2015),
no. 2, 763–782 (arxiv).
 Amenable groups without finitely presented amenable
covers, with M.Benli, P. de la Harpe, (Bull.
Math. Sci. (2013) 3:73–131)
 On the lattice of subgroups of the lamplighter group,
with R.Kravchenko, International Journal
of Algebra and Application, 24, (2014), no. 6, 837877 (arxiv)
 On the Gap Conjecture concerning group growth, Bulletin of
Mathematical Sciences, 2014, no.4,
113128 (arxiv).

On the condensation property of the lamplighter groups and groups of intermediate growth, with M.G.Benli, Algebra Discrete Math.
17
(2014), no. 2, 222–231.
 Milnor's Problem on the Growth of Groups and its
Consequences In: Frontiers in Complex Dynamics. In Celebration of John
Milnor's 80th Birthday, volume 51 of Princeton Mathematical Series,
Princeton University Press, Princeton and Oxford, 2014, 705773. (arxiv)
 On Algebraic Properties of Topological Full Groups,
with K. Medynets, Matemat.
Sbornik , 205, (2014), no.6, 87108 (arxiv)
 On the condensation property of the Lamplighter groups
and groups of Intermediate growth, with M.Benli, Algebra Discrete
Math., v.17 (2014), no.2, 222–231 ,
(arxiv)
 Diameters, distortion and eigenvalues, with Piotr Nowak, European
J. Combin. 33
(2012),
no.
7, 1574–1587 (arxiv).
 Ergodic properties of boundary actions and Nielsen's
Method
with V. Kaimanovich and T. SmirnovaNagnibeda,
Adv.
Math. 230
(2012),
no.
3, 1340–1380 (arxiv).
 Some topics of dynamics of group actions on rooted trees., The
Proceedings of the Steklov Institute of Math.,
v. 273 (2011), 1118. (file)
 On a question of Wiegold and
torsion images of Coxeter groups , Algebra Discrete Math., (2009), no.4,
7896.(arxiv)
 On Dehn functions of infinite
presentations of groups, with S.Ivanov,
GAFA Geometric and Functional Analysis, 2009, 18411847 (arxiv)
 Groups of Intermediate Growth, an Introduction, with I.Pak,
L'Enseignement Mathematique,
54 (2008), 251272 (pdf)
 Schreier spectrum of the Hanoi
towers group on three pegs, with Z.Sunic, Proceedings of Symposia in Pure
Mathematics, 77 (2008), 183198 (arxiv)
 Homomorphic images of branch groups, and Serre's property (FA), with T.Delzant,
(arxiv)
in Geometry and Dynamics of Groups and Spaces. In Memory of Alexander Reznikov. Progress in Mathematics Series, Vol. 265. Kapranov, M.; Kolyada, S.; Manin, Y.I.; Moree, P.; Potyagailo, L.A. (Eds.), Birkhauser,
2008, Approx. 800 p. 351374.
 Classification of groups generated by 3state automata
over a 2letter alphabet, (with I.Bondarenko, R.Kravchenko, Y.Muntyan,
V.Nekrashevych,
D.Savchuk
and Z.Sunik),
Algebra Discrete Math. 2008, no. 1, 1163 (arXiv)
 Selfsimilar groups, operator algebras and Schur complements, with V.Nekrashevych, (arxiv) Journal of
Modern Dynamics, V.1, n.3, 2007, 323370.
 Selfsimilarity and branching in group theory, with Z.Sunic,
London
Mathematical Society Lecture Note Series, 339, 2007, 3695. (pdf)
 The Spectral Problem, Substitutions and Iterated Monodromy, with Z.Sunic and D.Savchuk,
(arxiv)
CRM Proceedings and Lecture Notes 42 (2007), American Mathematical
Society, 225248.
 Asymptotic aspects of Schreier
graphs and Hanoi Towers groups, with Zoran
Sunik, Comptes Rendus Mathematique, Academie des
Sciences Paris, 342 (2006), no. 8, 545550. (arxiv)
 Solved and
Unsolved Problems Around One Group, in Infinite
Groups: Geometric, Combinatorial and Dynamical Aspects. Progress in
Mathematics Series, Vol. 248. Bartholdi, L.; CeccheriniSilberstein,
T.; SmirnovaNagnibeda, T.; Zuk,
A. (Eds.). 2005, 413 p., Hardcover A Birkhauser
book
 Amenable Actions
of Nonamenable Groups, with Volodymyr Nekrashevych, in Representation Theory,
Dynamical Systems, Combinatorial and Algorithmic Methods. Part 13.
"Zapiski Nauchnyh
Seminarov POMI" Series, VOL. 326 (2005),
pages 8596
 The Group of Automorphisms of a 3generated 2group of Intermediate
Growth, with Said Sidki, International
Journal of Algebra and Computation Vol. 14, Nos. 5 & 6 (2004) 110
Selected papers
 From
fractal groups to fractal sets, with Laurent Bartholdi and Volodymyr V. Nekrashevych, Fractals in Graz
(Peter Grabner and Wolfgang Woess
(Technische~University Graz), eds.), Trends in
Mathematics, Birkhaser Verlag,
Basel, 2003, pages 25118
 Branch groups (with Laurent Bartholdi and Zoran Sunik),
Handbook
of Algebra vol 3, PDF file
 Sousgroupes paraboliques et
representations de groupes branches,
with Laurent Bartholdi, C. R. Acad. Sci.
332 (2001), no. 9, pages 789794
 Spectra
of noncommutative dynamical systems and graphs related to fractal groups,
with Laurent Bartholdi, C. R. Acad. Sci.
331 (2000), no. 6, pages 429434
 On Parabolic
Subgroups and Hecke Algebras of Some Fractal
Groups, with Laurent Bartholdi, Serdica
Math. J. 28 (2002), pages 4790
 On
the Spectrum of Hecke Type Operators related to
some Fractal Groups, with Laurent Bartholdi, Tr. Mat. Inst. Steklova 231 (2000), Din. Sist., Avtom. i
Beskon. Gruppy, pages
545; translation in Proc.
Steklov Inst. Math. 2000, no. 4 (231), pages
141
 Lie
methods in Growth of Groups and Groups of finite Width, with
Laurent Bartholdi, LMS Lect. Note Ser. 275 (2000), pages 127
 On a
question of Atiyah, with P. Linnell, T. Schick, A. Zuk,
C.R. Acad. Sci. Paris t.331 (2000), 662668.
 The Ihara
zeta function and spectral measure for infinite graphs, with A. Zuk, the KNS spectral measure and integrable
maps, Random walks and geometry, 141180, Walter de Gruyter
GmbH & Co. KG, Berlin, 2004.
 Automata,
dynamical systems and infinite groups, with V.V.Nekrashevich,
V.I.Sushchanskii, Proc. Steklov
Inst. Math. v.231 (2000), 134214.
 Amenability and
paradoxical decompositions for pseudogroups and
for discrete metric spaces, with T.CeccheriniSilberstein
and P. de la Harpe, Tr. Mat. Inst. Steklova 224 (1999), Algebra. Topol.
Differ. Uravn. i ikh Prilozh., 68111; translation in Proc. Steklov Inst. Math. 1999, no. 1 (224), 5797
 On the
asymptotic spectrum of random walks on infinite families of graphs , with A.Zuk,
Random walks and discrete potential theory (Cortona,
1997), Sympos. Math., XXXIX, Cambridge Univ.
Press, Cambridge, (1999), 188204.
Undergraduate research
Full list of
publications and dissertations
Undergraduate research
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