## Teaching## Research## Publications## Meetings## Main |
## Preprints*Growth of etale groupoids and simple algebras*.*Self-similar groups, automatic sequences, and unitriangular representations*, (with R. Grigorchuk, Y. Leonov, and V. Sushchansky).*Finitely presented groups associated with expanding maps*.*Extensions of amenable groups by recurrent groupoids,*(with Kate Juschenko and Mikael de la Salle).*Smale spaces with virtually nilpotent splitting**Hyperbolic groupoids and duality*(to appear in Memoirs of the A.M.S.)
## Selected publications*Hyperbolic groupoids: metric and measure*, Groups, Geometry, and Dynamics, vol.**8**, No. 3, (2014), pp. 883-932. (preliminary version)*An uncountable family of 3-generated groups with isomorphic profinite completions*, International Journal of Algebra and computation, vol. 24, No. 01, (2014), pp. 33-46. (preliminary version)*Combinatorial models of expanding dynamical systems*, Ergodic Theory and Dynamical Systems, vol. 34, (2014), pp. 938-985. (preliminary version)*The Julia set of a post-critically finite endomorphism of PC^2*, Journal of Modern Dynamics, vol.**6**, No. 3, (2012), pp. 327-375. extended preliminary version*On a family of Schreier graphs of intermediate growth associated with a self-similar group*, European Journal of Combinatorics, vol.**33**, No. 7, 2012, pp. 1408-1421. (with I. Bondarenko, T. Ceccherini-Silberstein, A. Donno) (arxiv version)*Iterated monodromy groups*"Groups St Andrews 2009 in Bath", Vol. 1, London Mathematical Society Lecture Note Series (No. 387), 2011, pp. 41-93 (preliminary version)- Scale-invariant groups, Groups, Geometry, and Dynamics,
**5**, (2011), No. 1, pp. 139-167. (with Gábor Pete) - Diagonal direct limits of finite symmetric and alternating groups., Algebra and Discrete Math.,
**10**, (2010), No. 1, pp. 67-87 (with Y.Lavrenyuk and V. Sushchansky). - Free subgroups in groups acting on rooted trees, Groups, Geometry, and Dynamics,
**4**, (2010), No. 4, pp. 847-862. -
On amenability of automata groups, Duke
Mathematical Journal,
**154**, (2010), No 3, p. 575-598. (With Laurent Bartholdi and Vadim Kaimanovich.) *A group of non-uniform exponential growth locally isomorphic to IMG(z^2+i),*Transactions of the AMS,**362**, (2010), p. 389-398.*C*-algebras and self-similar groups*, Journal für die reine und angewandte Mathematik,**630**(2009), p. 59-123.*Combinatorics of polynomial iterations*, in*Complex Dynamics -- Families and Friends*, D. Schleicher ed., A K Peters, 2009, p. 169-214. (a prelim. version)*Symbolic dynamics and self-similar groups*, "Holomorphic Dynamics and Renormalization: A Volume in Honour of John Milnor's 75th Birthday", volume 53 of*Fields Institute Communications.*, 2008, p. 25-73.*Groups and analysis on fractals*, "Analysis on Graphs and its Applications", P. Exner, J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev eds., vol. 77 of*Proceedings of Symposia in Pure Mathematics*, A.M.S., 2008, p. 143-170 (with Alexander Teplyaev).-
*Iterated monodromy groups of quadratic polynomials, I*, Groups, Geometry, and Dynamics,**2**, (2008), No. 3, p. 309-336 (with Laurent Bartholdi), (arXiv version). -
*A minimal Cantor set in the space of 3-generated groups*, Geom. Dedicata,**124**, (2007), No. 2, p. 153-190. -
*Self-Similar Groups, Operator Algebras and Schur Complement*, Journal of Modern Dynamics,**1**, (2007), No. 3, p. 323-370. (with Rostislav Grigorchuk), (arXiv version). *Self-similar groups and their geometry*, São Paulo Journal of Mathematical Sciences,**1**, (2007), No. 1, p. 41-96.-
*On classification of inductive limits of direct products of alternating groups*, Journal of the London Mathematical Society,**75**, (2007), No. 1, p. 146-162. (with Yaroslav Lavrenyuk). -
*Thurston equivalence of topological polynomials*, Acta Math.,**197**, (2006), p. 1-51. (with Laurent Bartholdi), (arXiv version). - Self-similar groups,
volume 117
of
*Mathematical Surveys and Monographs*. Amer. Math. Soc., Providence, RI, 2005. -
*Self-similar inverse semigroups and Smale spaces*, International Journal of Algebra and Computation,**16**, no 5, (2006), p. 849-874. -
*Automata, groups, limit spaces, and tilings*, J. Algebra,**305**, (2006), no. 2, p. 629-663, (with André Henriques and Laurent Bartholdi), (arXiv version). *Amenable actions of nonabenable groups*, Zapiski Nauchnyh Seminarov POMI, (2005), p. 85-95, and Journal of Mathematical Sciences,**140**, (2006), no. 3, p. 391-397 (with Rostislav Grigorchuk).-
*Cuntz-Pimsner algebras of group actions*, Journal of Operator Theory,**52**, (2004), no. 2, p. 223-249. (preliminary version) -
*Dynamics of triangular transformations of sequences over finite alphabets*, Math. Notes,**73**, (2003), no. 3-4, p. 436-439 (with Eva Mochko and Vitaly Sushchanskii). *Post-critically finite self-similar groups*, Algebra and Discrete Mathematics,**2**, no 4, (2003) pp. 21-32. (with Evgen Bondarenko)*Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms*, In T.W. Müller, editor,*Groups: Topological, Combinatorial and Arithmetic Aspects*, volume 311 of*LMS Lecture Notes Series*, pages 375-404, 2004. (with S.Sidki).*From fractal groups to fractal sets*, In Peter Grabner and Wolfgang Woess, editors,*Fractals in Graz 2001*,*Analysis-Dynamics-Geometry-Stochastics*, volume 19 of*Trends in Mathematics*, Birkhäuser, (2003), pages 25-118 (with Laurent Bartholdi and Rostislav I. Grigorchuk). (see preliminary versions here and here).*Hyperbolic spaces from self-similar group actions*, Algebra and Discrete Mathematics,**2**, no 2, (2003), pp. 77-86.*Virtual endomorphisms of groups*, Algebra and Discrete Mathematics,**1**, no 1, (2002), pp. 88-128.-
*Rigidity of branch groups acting on rooted trees*, Geom. Dedicata,**89**, (2002), 159-179. (with Ya.Lavreniuk). -
*Conjugation in tree automorphism groups*, Int. J. of Algebra and Computation,**11,**(2001), no. 5, 529-547. (with P.W.Gawron and V.I.Sushchansky). *On confinal dynamics of rooted tree automorphisms*, Computational and Geometric Aspects of Modern Algebra (Michael Atkinson et al., ed.),*LMS Lecture Notes Series*, volume 275, Cambridge Univ. Press, Cambridge, 2000, pp. 229-246. (with V.I.Sushchanky).-
*Stabilizers of transitive actions on locally finite graphs*, International Journal of Algebra and Computation,**10,**(2000), no. 5, 591-602. *The group of asynchronous automata and rational homeomorphisms of the Cantor set*, Math. Notes,**67**, (2000), no. 5, 577-581 (with R. Grigorchuk).-
*Automata, dynamical systems and groups*, Proceedings of the Steklov Institute of Mathematics,**231**, (2000), 128-203. (with R. I. Grigorchuk and V.I.Sushchansky). *Commensurators of groups and reversible automata*, Dopov. Nats. Akad. Nauk Ukr., no 12, (2000), 36-39. (with Olga Macedonska and Vitali Sushchansky).*Uniformly bounded spaces*, Voprosy Algebry,**14**, (1999), 47-97.*Quasi-isometric hyperbolic groups are bi-Lipschitz equivalent*, Dokl. Nat. Akad. Nauk Ukraine, (1998), no. 1, 32-35.*On equivalence of nets in hyperbolic spaces*, Dokl. Nat. Akad. Nauk Ukraine, (1997), no. 11, 18-21.
Some of them can be found on arXiv.org ## Book reviews*Words: notes on verbal width in groups*, by Dan Segal. Bull. Amer. Math. Soc. 48 (2011) 491-494.*How groups grow*, by Avinoam Mann. Bull. Amer. Math. Soc. 50 (2013), 495-502.
## Co-authorsLaurent Bartholdi, Ievgen Bondarenko, Rostislav Grigorchuk, Kate Juschenko, Vadim Kaimanovich, Yaroslav Lavrenyuk, Gábor Pete, Mikael de la Salle, Vitaily Sushchanskyy, Alexander Teplyaev. |
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