Research

Area of Research: Geometric Group Theory, Discrete Mathematics
Research Interests: My main research interests are in the theory of self-similar groups, groups generated by finite automata, and related topics.

Selected Publications and Preprints

  1. I.Bondarenko, B.Kivva. Automaton groups and complete square complexes, 29 pages, 2017. (arXiv version)
  2. I.Bondarenko, D.D’Angeli, T.Nagnibeda. Ends of Schreier graphs and cut-points of limit spaces of self-similar groups, Journal of Fractal Geometry, Number 4, P. 369-424, 2017. (pdf,access)
  3. I.Bondarenko, D.D’Angeli, E.Rodaro. The lamplighter group Z_3\wr Z generated by a bireversible automaton, Communications in Algebra, Volume 44, Issue 12, P. 5257-5268, 2016. (arXiv version, access)
  4. I.Bondarenko. Self-similar groups and the zig-zag and replacement products of graphs, Journal of Algebra, Volume 434, P. 1-11, 2015. (arXiv version, access)
  5. I.Bondarenko. The word problem in Hanoi Towers groups, Algebra and Discrete Mathematics, Volume 17, Number 2, P. 248-255, 2014. (arXiv version, access)
  6. I.Bondarenko. Tilings of limit spaces of self-similar groups, Matematychni Studii, Volume 41, Number 2, P. 134-138, 2014. (pdf, access)
  7. I.Bondarenko, N.Bondarenko, S.Sidki, F.Zapata. On the conjugacy problem for finite-state automorphisms of regular rooted trees (with an appendix by Raphael M. Jungers), Groups, Geometry, and Dynamics, Volume 7, Issue 2, P. 323-355, 2013. (arXiv version, access)
  8. I.Bondarenko, I.Samoilovych. On finite generation of self-similar groups of finite type, International Journal of Algebra and Computation, Volume 23, Number 1, P. 69-79, 2013. (arXiv version, access)
  9. I.Bondarenko, R.Kravchenko. Finite-state self-similar actions of nilpotent groups, Geometriae Dedicata, Volume 163, Issue 1, P. 339-348, 2013. (arXiv version, access)
  10. I.Bondarenko. Growth of Schreier graphs of automaton groups, Mathematische Annalen, Volume 354, Number 2, P. 765-785, 2012. (arXiv version, access)
  11. I.Bondarenko, T.Ceccherini-Silberstein, A.Donno, V.Nekrashevych. On a family of Schreier graphs of intermediate growth associated with a self-similar group, European Journal of Combinatorics, Volume 33, Issue 7, P. 1408-1421, 2012. (arXiv version, access)
  12. I.Bondarenko, R.Kravchenko. On Lebesgue measure of integral self-affine sets, Discrete & Computational Geometry, Volume 46, Number 2, P. 389-393, 2011. (arXiv version, access)
  13. I.Bondarenko, R.Kravchenko. Graph-directed systems and self-similar measures on limit spaces of self-similar groups, Advances in Mathematics, Volume 226, Issue 3, P. 2169-2191, 2011. (arXiv version, access)
  14. I.Bondarenko. Finite generation of iterated wreath products, Archiv der Mathematik, Volume 95, Number 4, P. 301-308, 2010. (arXiv version, access)
  15. I.Bondarenko. Dynamics of piecewise linear maps and sets of nonnegative matrices, Linear Algebra and its Applications, Volume 431, No. 5-7, P. 495-510, 2009. (arXiv version, access)
  16. I.Bondarenko, R.Grigorchuk, R.Kravchenko, Y.Muntyan, V.Nekrashevych, D.Savchuk, Z.Sunik. On classification of groups generated by 3-state automata over a 2-letter alphabet, Algebra and Discrete Mathematics, Number 1, P. 1-163, 2008. (arXiv version, access)
  17. I.Bondarenko. Groups generated by bounded automata and their Schreier graphs, Texas A&M University, Ph.D. Dissertation, 154pp, 2007. (pdf)
  18. I.Bondarenko, D.Savchuk. On Sushchansky p-groups, Algebra and Discrete Mathematics, Number 2, P. 22-42, 2007. (arXiv version, access)
  19. I.Bondarenko. Schreier graphs of iterated monodromy groups of sub-hyperbolic quadratic polynomials (in ukrainian), Matematychni Studii, Volume 22, Number 2, P. 159-175, 2004. (access)
  20. I.Bondarenko, V.Nekrashevych Post-critically finite self-similar groups, Algebra and Discrete Mathematics, Number 4, P. 21-32, 2003. (arXiv version, access)

Problems and Conjectures

Open Problems in Combinatorial and Geometric Group Theory

Self-Similarity and Branching in Group Theory, Problem List, Workshop, October 12-17, 2008. (pdf)

Self-Similar Groups and Conformal Dynamics, Problem List, AIM workshop, June 5-9, 2006. (pdf)

Problem List from the paper “Branch groups” of L.Bartholdi, R.I.Grigorchuk, and Z.Sunik. (pdf)

Problem List from the paper “Automata, dynamical systems and groups” of V.V.Nekrashevych, R.I.Grigorchuk, and V.I.Sushchansky. (pdf)

Solved and Unsolved Problems Around One Group by R.Grigorchuk. (pdf, ps.gz)