## Teaching## Research## Publications## Talks## Main |
## Preprints*On topological full groups of Z^d-actions*(with M. Chornyi and K. Juschenko)*Smale spaces with virtually nilpotent splitting*
## Publications-
Palindromic subshifts and simple periodic groups of intermediate growth,
*Annals of Mathematics*, vol.**187**, (2018), No. 3, pp. 667-719. (arXiv version). -
Simple groups of dynamical origin,
to appear in
*Ergodic Theory and Dynamical Systems*, (arXiv version). -
Finitely presented groups associated with expanding maps,
in "Geometric and Cohomological Group Theory",
P.H. Kropholler, I.J. Leary, C. Martínez-Pérez, B. Nucinkis (eds),
*London Mathematical Society Lecture Note Series*, (No. 444), 2017, pp. 115-171, (arXiv version). -
Mating, paper folding, and an endomorphism of PC^2,
*Conformal Geometry and Dynamics*, vol.**20**, (2016), pp. 303-358. -
Extensions of amenable groups by recurrent groupoids,
*Inventiones Mathematicae*, vol.**206**, (2016), No. 3, pp. 837-867, (with Kate Juschenko and Mikael de la Salle), (arXiv version). -
Growth of etale groupoids and simple algebras,
*International Journal of Algebra and computation*,**26**, (2016), No. 2, pp. 375-397, (arXiv version). -
Self-similar groups, automatic sequences, and unitriangular representations,
*Bulletin of Mathematical Sciences*, vol.**6**, 2016, no 2, pp. 231-285, (with R. Grigorchuk, Y. Leonov, and V. Sushchansky), (arXiv version). -
From self-similar groups to self-similar sets and spectra,
Fractal Geometry and Stochastics V,
*Progress in Probability*,**70**(2015), pp. 175-207, (with R. Grigorchuk and Z. Sunic). -
Hyperbolic groupoids and duality,
*Memoirs of the American Mathematical Society*, vol.**237**, No. 1122, (2015). -
Hyperbolic groupoids: metric and measure,
*Groups, Geometry, and Dynamics*, vol.**8**, No. 3, (2014), pp. 883-932, (arXiv 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, (arXiv version). -
Combinatorial models of expanding dynamical systems,
*Ergodic Theory and Dynamical Systems*, vol.**34**, (2014), pp. 938-985, (arXiv 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 arXiv 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). -
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,
*Complex Dynamics - Families and Friends*, D. Schleicher ed., A K Peters, 2009, p. 169-214, (preliminary 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,
*Geometriae 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 Mathematica*,**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,
*Journal of Algebra*,**305**, (2006), no. 2, p. 629-663, (with André Henriques and Laurent Bartholdi), (arXiv version). -
Amenable actions of nonabenable groups,
*Journal of Mathematical Sciences*,**140**, (2006), no. 3, p. 391-397, (with Rostislav Grigorchuk), (preliminary version). -
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,
*Groups: Topological, Combinatorial and Arithmetic Aspects*, T.W. Müller, editor, volume 311 of*LMS Lecture Notes Series*, pages 375-404, 2004, (with S.Sidki). -
From fractal groups to fractal sets,
*Fractals in Graz 2001*,*Analysis-Dynamics-Geometry-Stochastics*, Peter Grabner and Wolfgang Woess, editors, 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,
*Geometriae Dedicata*,**89**, (2002), 159-179, (with Ya.Lavreniuk). -
Conjugation in tree automorphism groups,
*International Journal 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,
*Mathematical 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,
*Dopovidi Natsionalnoi Akademii Nauk Ukrainy*, 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,
*Dopovidi Natsionalnoi Akademii Nauk Ukrainy*, (1998), no. 1, 32-35. -
On equivalence of nets in hyperbolic spaces,
*Dopovidi Natsionalnoi Akademii Nauk Ukrainy*, (1997), no. 11, 18-21.
Some of them can be found on arXiv.org ## Book reviews*Metric geometry of locally compact groups*by Yves Cornulier and Pierre de la Harpe. Bull. Amer. Math. Soc. (2018), electronic version.*How groups grow*, by Avinoam Mann. Bull. Amer. Math. Soc. 50 (2013), 495-502.*Words: notes on verbal width in groups*, by Dan Segal. Bull. Amer. Math. Soc. 48 (2011) 491-494.
## Co-authorsLaurent Bartholdi, Ievgen Bondarenko, Rostislav Grigorchuk, Kate Juschenko, Vadim Kaimanovich, Yaroslav Lavrenyuk, Gábor Pete, Mikael de la Salle, Vitaily Sushchanskyy, Alexander Teplyaev. |
---|