Teaching

Research

Publications

Meetings

Main


Preprints

  1. Finitely presented groups associated with expanding maps. pdficon
  2. Extensions of amenable groups by recurrent groupoids, (with Kate Juschenko and Mikael de la Salle). pdficon
  3. An uncountable family of 3-generated groups with isomorphic profinite completions pdficon
  4. Smale spaces with virtually nilpotent splitting pdficon
  5. Hyperbolic groupoids: metric and measure pdficon
  6. Hyperbolic groupoids and duality pdficon (to appear in Memoirs of the A.M.S.)

Selected publications

  1. Combinatorial models of expanding dynamical systems, to appear in Ergodic Theory and Dynamical Systems. (preliminary version)
  2. 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
  3. 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)
  4. 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)
  5. Scale-invariant groups, Groups, Geometry, and Dynamics, 5, (2011), No. 1, pp. 139-167. (with Gábor Pete)
  6. 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).
  7. Free subgroups in groups acting on rooted trees, Groups, Geometry, and Dynamics, 4, (2010), No. 4, pp. 847-862.
  8. On amenability of automata groups, Duke Mathematical Journal, 154, (2010), No 3, p. 575-598. (With Laurent Bartholdi and Vadim Kaimanovich.)
  9. A group of non-uniform exponential growth locally isomorphic to IMG(z^2+i), Transactions of the AMS, 362, (2010), p. 389-398.
  10. C*-algebras and self-similar groups, Journal für die reine und angewandte Mathematik, 630 (2009), p. 59-123.
  11. Combinatorics of polynomial iterations, in Complex Dynamics -- Families and Friends, D. Schleicher ed., A K Peters, 2009, p. 169-214. (a prelim. version)
  12. 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.
  13. 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).
  14. Iterated monodromy groups of quadratic polynomials, I, Groups, Geometry, and Dynamics, 2, (2008), No. 3, p. 309-336 (with Laurent Bartholdi), (arXiv version).
  15. A minimal Cantor set in the space of 3-generated groups, Geom. Dedicata, 124, (2007), No. 2, p. 153-190.
  16. Self-Similar Groups, Operator Algebras and Schur Complement, Journal of Modern Dynamics, 1, (2007), No. 3, p. 323-370. (with Rostislav Grigorchuk), (arXiv version).
  17. Self-similar groups and their geometry, São Paulo Journal of Mathematical Sciences, 1, (2007), No. 1, p. 41-96.
  18. 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).
  19. Thurston equivalence of topological polynomials, Acta Math., 197, (2006), p. 1-51. (with Laurent Bartholdi), (arXiv version).
  20. Self-similar groups, volume 117 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2005.
  21. Self-similar inverse semigroups and Smale spaces, International Journal of Algebra and Computation, 16, no 5, (2006), p. 849-874.
  22. Automata, groups, limit spaces, and tilings, J. Algebra, 305, (2006), no. 2, p. 629-663, (with André Henriques and Laurent Bartholdi), (arXiv version).
  23. 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).
  24. Cuntz-Pimsner algebras of group actions, Journal of Operator Theory, 52, (2004), no. 2, p. 223-249. (preliminary version)
  25. 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).
  26. Post-critically finite self-similar groups, Algebra and Discrete Mathematics, 2, no 4, (2003) pp. 21-32. (with Evgen Bondarenko)
  27. 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).
  28. 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).
  29. Hyperbolic spaces from self-similar group actions, Algebra and Discrete Mathematics, 2, no 2, (2003), pp. 77-86.
  30. Virtual endomorphisms of groups, Algebra and Discrete Mathematics, 1, no 1, (2002), pp. 88-128.
  31. Rigidity of branch groups acting on rooted trees, Geom. Dedicata, 89, (2002), 159-179. (with Ya.Lavreniuk).
  32. 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).
  33. 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).
  34. Stabilizers of transitive actions on locally finite graphs, International Journal of Algebra and Computation, 10, (2000), no. 5, 591-602.
  35. The group of asynchronous automata and rational homeomorphisms of the Cantor set, Math. Notes, 67, (2000), no. 5, 577-581 (with R. Grigorchuk).
  36. Automata, dynamical systems and groups, Proceedings of the Steklov Institute of Mathematics, 231, (2000), 128-203. (with R. I. Grigorchuk and V.I.Sushchansky).
  37. Commensurators of groups and reversible automata, Dopov. Nats. Akad. Nauk Ukr., no 12, (2000), 36-39. (with Olga Macedonska and Vitali Sushchansky).
  38. Uniformly bounded spaces, Voprosy Algebry, 14, (1999), 47-97.
  39. Quasi-isometric hyperbolic groups are bi-Lipschitz equivalent, Dokl. Nat. Akad. Nauk Ukraine, (1998), no. 1, 32-35.
  40. 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

  1. Words: notes on verbal width in groups, by Dan Segal. Bull. Amer. Math. Soc. 48 (2011) 491-494.
  2. How groups grow, by Avinoam Mann. Bull. Amer. Math. Soc. 50 (2013), 495-502.

Co-authors

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