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Area of Research: Geometric Group Theory, Discrete Mathematics
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Research Interests: My main research interests are in the theory of self-similar groups, groups generated by finite automata, and related topics.
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Selected Publications and Preprints
- I.Bondarenko, B.Kivva. Automaton groups and complete square complexes, 29 pages, 2017. (arXiv version)
- 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)
- 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)
- 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)
- I.Bondarenko. The word problem in Hanoi Towers groups, Algebra and Discrete Mathematics, Volume 17, Number 2, P. 248-255, 2014. (arXiv version, access)
- I.Bondarenko. Tilings of limit spaces of self-similar groups, Matematychni Studii, Volume 41, Number 2, P. 134-138, 2014. (pdf, access)
- 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)
- 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)
- 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)
- I.Bondarenko. Growth of Schreier graphs of automaton groups, Mathematische Annalen, Volume 354, Number 2, P. 765-785, 2012. (arXiv version, access)
- 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)
- 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)
- 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)
- I.Bondarenko. Finite generation of iterated wreath products, Archiv der Mathematik, Volume 95, Number 4, P. 301-308, 2010. (arXiv version, access)
- 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)
- 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)
- I.Bondarenko. Groups generated by bounded automata and their Schreier graphs, Texas A&M University, Ph.D. Dissertation, 154pp, 2007. (pdf)
- I.Bondarenko, D.Savchuk. On Sushchansky p-groups, Algebra and Discrete Mathematics, Number 2, P. 22-42, 2007. (arXiv version, access)
- 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)
- 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
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Open Problems in Combinatorial and Geometric Group Theory
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Self-Similarity and Branching in Group Theory, Problem List, Workshop, October 12-17, 2008. (pdf)
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Self-Similar Groups and Conformal Dynamics, Problem List, AIM workshop, June 5-9, 2006. (pdf)
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Problem List from the paper “Branch groups” of L.Bartholdi, R.I.Grigorchuk, and Z.Sunik. (pdf)
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Problem List from the paper “Automata, dynamical systems and groups” of V.V.Nekrashevych, R.I.Grigorchuk, and V.I.Sushchansky. (pdf)
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Solved and Unsolved Problems Around One Group by R.Grigorchuk. (pdf, ps.gz)
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