Teaching

Research

Publications

Talks

Main


Preprints

  1. On topological full groups of Z^d-actions (with M. Chornyi and K. Juschenko) pdficon
  2. Smale spaces with virtually nilpotent splitting pdficon

Publications

  1. Palindromic subshifts and simple periodic groups of intermediate growth, Annals of Mathematics, vol. 187, (2018), No. 3, pp. 667-719. (arXiv version).
  2. Simple groups of dynamical origin, to appear in Ergodic Theory and Dynamical Systems, (arXiv version).
  3. 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).
  4. Mating, paper folding, and an endomorphism of PC^2, Conformal Geometry and Dynamics, vol. 20, (2016), pp. 303-358.
  5. 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).
  6. Growth of etale groupoids and simple algebras, International Journal of Algebra and computation, 26, (2016), No. 2, pp. 375-397, (arXiv version).
  7. 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).
  8. 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).
  9. Hyperbolic groupoids and duality, Memoirs of the American Mathematical Society, vol. 237, No. 1122, (2015).
  10. Hyperbolic groupoids: metric and measure, Groups, Geometry, and Dynamics, vol. 8, No. 3, (2014), pp. 883-932, (arXiv version).
  11. 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).
  12. Combinatorial models of expanding dynamical systems, Ergodic Theory and Dynamical Systems, vol. 34, (2014), pp. 938-985, (arXiv version).
  13. 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).
  14. 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).
  15. 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).
  16. Scale-invariant groups, Groups, Geometry, and Dynamics, 5, (2011), No. 1, pp. 139-167, (with Gábor Pete).
  17. Free subgroups in groups acting on rooted trees, Groups, Geometry, and Dynamics, 4, (2010), No. 4, pp. 847-862.
  18. On amenability of automata groups, Duke Mathematical Journal, 154, (2010), No 3, p. 575-598, (with Laurent Bartholdi and Vadim Kaimanovich).
  19. A group of non-uniform exponential growth locally isomorphic to IMG(z^2+i), Transactions of the AMS, 362, (2010), p. 389-398.
  20. C*-algebras and self-similar groups, Journal für die reine und angewandte Mathematik, 630 (2009), p. 59-123.
  21. Combinatorics of polynomial iterations, Complex Dynamics - Families and Friends, D. Schleicher ed., A K Peters, 2009, p. 169-214, (preliminary version).
  22. 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.
  23. 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).
  24. Iterated monodromy groups of quadratic polynomials, I, Groups, Geometry, and Dynamics, 2, (2008), No. 3, p. 309-336, (with Laurent Bartholdi), (arXiv version).
  25. A minimal Cantor set in the space of 3-generated groups, Geometriae Dedicata, 124, (2007), No. 2, p. 153-190.
  26. Self-Similar Groups, Operator Algebras and Schur Complement, Journal of Modern Dynamics, 1, (2007), No. 3, p. 323-370, (with Rostislav Grigorchuk), (arXiv version).
  27. Self-similar groups and their geometry, São Paulo Journal of Mathematical Sciences, 1, (2007), No. 1, p. 41-96.
  28. 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).
  29. Thurston equivalence of topological polynomials, Acta Mathematica, 197, (2006), p. 1-51. (with Laurent Bartholdi), (arXiv version).
  30. Self-similar groups, volume 117 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2005.
  31. Self-similar inverse semigroups and Smale spaces, International Journal of Algebra and Computation, 16, no 5, (2006), p. 849-874.
  32. Automata, groups, limit spaces, and tilings, Journal of Algebra, 305, (2006), no. 2, p. 629-663, (with André Henriques and Laurent Bartholdi), (arXiv version).
  33. Amenable actions of nonabenable groups, Journal of Mathematical Sciences, 140, (2006), no. 3, p. 391-397, (with Rostislav Grigorchuk), (preliminary version).
  34. Cuntz-Pimsner algebras of group actions, Journal of Operator Theory, 52, (2004), no. 2, p. 223-249, (preliminary version).
  35. 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).
  36. Post-critically finite self-similar groups, Algebra and Discrete Mathematics, 2, no 4, (2003) pp. 21-32, (with Evgen Bondarenko).
  37. 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).
  38. 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).
  39. Hyperbolic spaces from self-similar group actions, Algebra and Discrete Mathematics, 2, no 2, (2003), pp. 77-86.
  40. Virtual endomorphisms of groups, Algebra and Discrete Mathematics, 1, no 1, (2002), pp. 88-128.
  41. Rigidity of branch groups acting on rooted trees, Geometriae Dedicata, 89, (2002), 159-179, (with Ya.Lavreniuk).
  42. 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).
  43. 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).
  44. Stabilizers of transitive actions on locally finite graphs, International Journal of Algebra and Computation, 10, (2000), no. 5, 591-602.
  45. The group of asynchronous automata and rational homeomorphisms of the Cantor set, Mathematical Notes, 67, (2000), no. 5, 577-581, (with R. Grigorchuk).
  46. Automata, dynamical systems and groups, Proceedings of the Steklov Institute of Mathematics, 231, (2000), 128-203, (with R. I. Grigorchuk and V.I.Sushchansky).
  47. Commensurators of groups and reversible automata, Dopovidi Natsionalnoi Akademii Nauk Ukrainy, no 12, (2000), 36-39, (with Olga Macedonska and Vitali Sushchansky).
  48. Uniformly bounded spaces, Voprosy Algebry, 14, (1999), 47-97.
  49. Quasi-isometric hyperbolic groups are bi-Lipschitz equivalent, Dopovidi Natsionalnoi Akademii Nauk Ukrainy, (1998), no. 1, 32-35.
  50. 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

  1. Metric geometry of locally compact groups by Yves Cornulier and Pierre de la Harpe. Bull. Amer. Math. Soc. (2018), electronic version.
  2. How groups grow, by Avinoam Mann. Bull. Amer. Math. Soc. 50 (2013), 495-502.
  3. Words: notes on verbal width in groups, by Dan Segal. Bull. Amer. Math. Soc. 48 (2011) 491-494.

Co-authors

Laurent Bartholdi, Ievgen Bondarenko, Rostislav Grigorchuk, Kate Juschenko, Vadim Kaimanovich, Yaroslav Lavrenyuk, Gábor Pete, Mikael de la Salle, Vitaily Sushchanskyy, Alexander Teplyaev.