Research interests

Groups generated by automata, contracting and branch groups. Algorithmic aspects of self-similar groups. Developing a software for computations in group theory. Schreier graphs. Amenability of groups. Random walks on groups and graphs.

• CV
• Research statement
• Teaching statement

Education

Publications

• "Automata generating free products of groups of order 2" (with Y. Vorobets), preprint, 19pp., 2008, (arXiv)
• "Some graphs related to Thompson's group F", Trends in Mathematics (Birkhauser), edited by O.Bogopolski, I.Bumagin, O.Kharlampovich and E.Ventura, 20pp., 2008, to appear (arXiv)
• "Classification of groups generated by 3-state automata over a 2-letter alphabet" (with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych and Z. Sunic), Algebra and Discrete Mathematics (2008) 1, 1-163. (arXiv, free access)
• "Groups generated by 3-state automata over a 2-letter alphabet, II" (with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych and Z. Sunic), J. Math. Sci. (New York), to appear, 2007 (arXiv)
• "Groups generated by 3-state automata over a 2-letter alphabet, I" (with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych and Z. Sunic), Sao Paulo Journal of Mathematical Sciences, 1 (2007), no.1, 1-40 (arXiv)
• "The spectral problem, substitutions and iterated monodromy" (with R. Grigorchuk and Z. Sunic), CRM Proceedings and Lecture Notes 42 (2007), 225-248, (arXiv)
• "On Sushchansky p-groups" (with I. Bondarenko), Algebra Discrete Math., 2007, no. 2, 22-42 (arXiv)
• "On word problem in contracting automorphism groups of rooted trees", Bulletin of the University of Kiev, Series: Physics & Mathematics, 2003, #1, 51-56 (pdf)

Software

• Package AutomGrp for computations in groups and semigroups generated by automata or given by wreath recursion for GAP system (joint with Y. Muntyan)
• Script related to the classification of groups generated by 3-state automata over 2-letter alphabet

Reports

• "About classification of groups generated by automata with three states over an alphabet with two letters, and about some questions concerning these groups" (with I. Bondarenko, R. Grigorchuk, R. Kravchenko, Y. Muntyan, V. Nekrashevych and Z. Sunic), Bulletin of Chernivtsi National University, Mathematics V.336--337 (2007),29--39

Presentations

• "Graphs related to Thompson's group F", colloquium at SUNY Binghamton, February 5, 2009 (pdf)
• "GAP package AutomGrp for computations in self-similar groups and semigroups: functionality, examples and applications" at Self-similarity and Branching in Group Theory Workshop, Banff International Research Station, Banff, Alberta, Canada, October 12, 2008 (pdf)
• "GAP package AutomGrp for computations in groups and semigroups generated by automata" at Computational Group Theory and Cohomology, Grantham, United Kingdom, August 7, 2008 (pdf)
• "Self-similar groups isomorphic to free products of groups of order 2" at Group theory and complexity, Steklov Mathematical Institute, Moscow, July 17, 2008 (pdf)
• "Some graphs related to Thompson's group F" at Fields Workshop in Asymptotic Group Theory and Cryptography at Carleton University, December 14-16, 2007, (pdf)
• "On classification of groups generated by 3-state automata over 2-letter alphabet" at Groups and their actions, Bedlewo, Poland, July 1-7, 2007 (pdf)
• "Groups generated by 3-state automata over 2-letter alphabet" at Geometric Groups on the Gulf Coast, New Orleans, January 10, 2007 (pdf)
• "Automata groups from different points of view" at Graduate Student Seminar, Texas A&M, October 19, 2006 (pdf)
• "On Sushchansky p-groups" at The Victor Rothschild Memorial Symposium. The 10-th Midrasha Mathematicae in: "Asymptotic Group Theory". The Hebrew University of Jerusalem, The Institute for Advanced Studies, May 16, 2006 (pdf)
• "The Schreier graphs of the Thompson group F" at Geometric and Asymptotic Methods in Group Theory Workshop, Banff International Research Station, Banff, Canada, June 2005 (pdf)

Undergraduate Exposition

• (with N.Rudomino-Dusyatska) "Is gambling worth it?" (Ukrainian), In the world of Mathematics, V.5 (1999), #3, 77-82.
• (with N.Rudomino-Dusyatska) "About D. Grave and some of his works on probability theory", Abstracts of the Third Ukrainian-Scandinavian Conference in Probability Theory and mathematical Statistics. June 8-12, 1999, Kyiv, Ukraine.
• "Projecting points on the exponent" (Ukrainian), In the world of Mathematics, V.4 (1998), #4, 26-32.
• "Nobel Prize and Mathematicians" (Ukrainian), In the world of Mathematics, V.3 (1997), #4, 62-64.

Updated: June 02nd, 2009