Recent Papers
- On Simple Finitely Generated Amenable Groups, with K. Medynets,
(arxiv)
- Some topics of dynamics of group actions on rooted trees., The Proceedings of the Steklov Institute of Math., v. 273 (2011), 1-118.
(file)
- Diameters, distortion and eigenvalues, with Piotr Nowak, (Accepted) European Journal of Combinatorics (arxiv)
- Ergodic properties of boundary actions and Nielsen's Method with V. Kaimanovich and T. Smirnova-Nagnibeda, (Accepted) Advances in Mathematics (arxiv)
- On a question of Wiegold and torsion images of Coxeter groups., Algebra Disrete Math., (2009), no.4, 78-96.(arxiv)
- On Dehn functions of infinite presentations of groups, with S.Ivanov,
GAFA Geometric and Functional Analysis, 2009, 1841-1847 (arxiv)
- Groups of Intermediate Growth, an Introduction, with I.Pak,
L'Enseignement Mathématique, 54 (2008), 251-272 (pdf)
- Ergodic properties of boundary actions and Nielsen-Schreier theory, with V.Kaimanovich and
T.Nagnibeda,
preprint (arxiv)
- Schreier spectrum of the Hanoi towers group on three pegs, with Z.Sunic,
Proceedings of Symposia in Pure Mathematics, 77 (2008), 183-198 (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. 351-374.
- Classification of groups generated by 3-state automata over a 2-letter alphabet, (with I.Bondarenko,
R.Kravchenko, Y.Muntyan,
V.Nekrashevych, D.Savchuk and
Z.Sunik), Algebra Discrete Math. 2008, no. 1, 1-163 (arXiv)
- Self-similar groups, operator algebras and Schur complements, with V.Nekrashevych, (arxiv) Journal of Modern Dynamics, V.1, n.3, 2007, 323-370.
- Self-similarity and branching in group theory, with Z.Sunic, London Mathematical Society Lecture Note Series, 339, 2007, 36-95. (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, 225-248.
- Asymptotic
aspects of Schreier graphs and Hanoi Towers groups, with Zoran Sunik, Comptes
Rendus Mathématique, Académie des Sciences Paris, 342 (2006), no. 8, 545-550.
(arxiv)
- Solved and Unsolved Problems Around One Group, in
Infinite Groups: Geometric, Combinatorial and Dynamical Aspects.
Progress in Mathematics Series, Vol. 248. Bartholdi, L.;
Ceccherini-Silberstein, T.; Smirnova-Nagnibeda, T.; Zuk, A. (Eds.).
2005, 413 p., Hardcover
A Birkhäuser 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 85-96
- The Group of Automorphisms of a 3-generated 2-group of Intermediate Growth,
with Said Sidki, International Journal of Algebra and Computation Vol. 14, Nos. 5 & 6 (2004)
1-10
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 25-118
- Branch groups (with Laurent Bartholdi and Zoran Sunik),
Handbook of Algebra vol 3,
PDF file
- Sous-groupes paraboliques et representations de groupes branches,
with Laurent Bartholdi, C. R. Acad. Sci. 332 (2001), no. 9, pages 789-794
- Spectra of non-commutative dynamical systems and graphs related to fractal groups,
with Laurent Bartholdi, C. R. Acad. Sci. 331 (2000), no. 6, pages 429-434
- On Parabolic Subgroups and Hecke Algebras of Some Fractal Groups,
with Laurent Bartholdi, Serdica Math. J. 28 (2002), pages 47-90
- 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 5-45; translation in
Proc. Steklov Inst. Math. 2000, no. 4 (231), pages 1-41
- Lie methods in Growth of Groups and Groups of finite Width,
with Laurent Bartholdi, LMS Lect. Note Ser. 275 (2000), pages 1-27
- On a question of Atiyah,
with P. Linnell, T. Schick, A. Zuk, C.R. Acad. Sci. Paris t.331 (2000), 662-668.
- The Ihara zeta function and spectral measure for infinite graphs,
with A. Zuk, the KNS spectral measure and integrable maps, Random walks
and geometry, 141-180, 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), 134-214.
- Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces,
with T.Ceccherini-Silberstein and P. de la Harpe, Tr. Mat. Inst.
Steklova 224 (1999), Algebra. Topol. Differ. Uravn. i ikh Prilozh.,
68-111; translation in Proc. Steklov Inst. Math. 1999, no. 1 (224),
57-97
Undergraduate research
Full list of publications and dissertations
Undergraduate research
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