Research interests

Geometric and combinatorial group theory. Geometry of Out(F_n). Thompson's groups. Groups acting on rooted trees: self-similar, generated by automata, iterated monodromy groups, contracting and branch groups. Algorithmic aspects of self-similar groups. Developing software for computations in group theory. Free and relatively free groups. Low-dimensional topology.

• CV
• Research statement

Education

Publications

1. "Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set", preprint, 2012, (arXiv)
2. "On the geometry of a proposed curve complex analogue for Out(F_n)" (with L. Sabalka), submitted, 2011 (arXiv)
3. "On Restricting Subsets of Bases in Relatively Free Groups" (with L. Sabalka), to appear in IJAC, 2012, (arXiv)
4. "Automata generating free products of groups of order 2" (with Y. Vorobets), Journal of Algebra, V.336 (2011), Issue 1, 53-66, (arXiv | journal)
5. "Some graphs related to Thompson's group F", in Combinatorial and geometric group theory, Trends in Mathematics (Birkhauser), edited by O.Bogopolski, I.Bumagin, O.Kharlampovich and E.Ventura, 279-296, 2010, (arXiv)
6. "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), Journal of Mathematical Sciences, V. 156 (2009), Number 1, 187-208, (arXiv | journal)
7. "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 | journal)
8. "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, V.1 (2007), no.1, 1-40 (arXiv)
9. "The spectral problem, substitutions and iterated monodromy" (with R. Grigorchuk and Z. Sunic), CRM Proceedings and Lecture Notes 42 (2007), 225-248, (arXiv)
10. "On Sushchansky p-groups" (with I. Bondarenko), Algebra Discrete Math., 2007, no. 2, 22-42 (arXiv)
11. "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

Undergraduate Exposition

1. (with N.Rudomino-Dusyatska) "Is gambling worth it?" (Ukrainian), In the world of Mathematics, V.5 (1999), #3, 77-82.
2. (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.
3. "Projecting points on the exponent" (Ukrainian), In the world of Mathematics, V.4 (1998), #4, 26-32.
4. "Nobel Prize and Mathematicians" (Ukrainian), In the world of Mathematics, V.3 (1997), #4, 62-64.

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