Research interests

Geometric and combinatorial group theory. Groups acting on rooted trees: self-similar, generated by automata, iterated monodromy groups, contracting and branch groups. Algorithmic aspects of self-similar groups. Group-based cryptography. Formal languages. p-adic dynamics. Thompson's groups. Developing software for computations in group theory. Dynamics of group actions. Free and relatively free groups.

• CV (August 2024)

Publications and Preprints

1. "Contracting Self-similar Groups in Group-Based Cryptography" (with D. Kahrobaei and A. Malik), Submitted (2024), 37 pages
   (arXiv)
2. "Liftable self-similar groups and scale groups" (with R. Grigorchuk), Submitted (2023), 50 pages
   (arXiv)
3. "Explicit Generators for the Stabilizers of Rational Points in Thompson’s Group F" (with K. Baker), Accepted to Groups, Geometry, and Dynamics (2023), 19 pages
   (arXiv)
4. "Solenoidal Maps, Automatic Sequences, Van Der Put Series, and Mealy-Moore Automata" (with R. Grigorchuk), Journal of the Australian Mathematical Society, 114 (2023), Issue 1, 78-109
   (arXiv | journal)
5. "Endomorphisms of regular rooted trees induced by the action of polynomials on the ring Z_d of d-adic integers" (with E. Ahmed), Journal of Algebra and its Applications, Vol. 19, No. 08, 2050154 (2020)
   (arXiv | journal)
6. "The lamplighter group of rank two generated by a bireversible automaton" (with E. Ahmed), Communications in Algebra, 47 (2019), Issue 8, 3340-3354
   (arXiv | journal)
7. "A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group (Extended Version)" (with Ines Klimann and Matthieu Picantin), International Journal of Foundations of Computer Science, 29, 297 (2018), 297–314
   (journal)
8. "Affine Automorphisms of Rooted Trees" (with S. Sidki), Geometriae Dedicata, 183 (2016), 195–213
   (arXiv | journal)
9. "Orbit automata as a new tool to attack the order problem in automaton groups" (with Ines Klimann and Matthieu Picantin), Journal of Algebra 445 (2016), 433–457
   (arXiv | journal)
10. "Ergodic decomposition of group actions on rooted trees" (with R. Grigorchuk), Proceedings of the Steklov Institute of Mathematics, V.292 (2016), Issue 1, 94–111
    (arXiv | journal)
11. "A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group" (with Ines Klimann and Matthieu Picantin), Lecture Notes in Computer Science, V. 9168, 313-325, The 19th International Conference on Developments in Language Theory (DLT 2015), 2015, 12 pp.
    (arXiv | journal)
12. "An Example of an Automatic Graph of Intermediate Growth" (with A. Miasnikov), Annals of Pure and Applied Logic, 166 (2015), no. 10, 1037–1048
    (arXiv | journal)
13. "Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set", Geometriae Dedicata, V.175 (2015), 355–372
    (arXiv | journal)
14. "Self-similar groups acting essentially freely on the boundary of the binary rooted tree" (with R. Grigorchuk), Contemporary Mathematics, V.611, 2014, 9–48
    (arXiv | volume)
15. "On the geometry of the edge splitting complex" (with L. Sabalka), Groups, Geometry, and Dynamics, 8 (2014), no. 2, 565–598
    (arXiv | journal)
16. "On Restricting Subsets of Bases in Relatively Free Groups" (with L. Sabalka), IJAC, V.22 (2012), no.4
    (arXiv | journal)
17. "Automata generating free products of groups of order 2" (with Y. Vorobets), Journal of Algebra, V.336 (2011), Issue 1, 53–66
    (arXiv | journal)
18. "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 | chapter)
19. "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)
20. "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 | script)
21. "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 | journal)
22. "The spectral problem, substitutions and iterated monodromy" (with R. Grigorchuk and Z. Sunic), CRM Proceedings and Lecture Notes 42 (2007), 225-248
    (arXiv)
23. "On Sushchansky p-groups" (with I. Bondarenko), Algebra Discrete Math., 2007, no. 2, 22-42
    (arXiv | journal)
24. "On word problem in contracting automorphism groups of rooted trees", Bulletin of the University of Kiev, Series: Physics & Mathematics, 2003, #1, 51-56
    (pdf)
25. "Submanifold Projection" (with L. Sabalka), preprint, 30 pp., 2012
    (arXiv)

Software

• Package AutomGrp for computations in groups and semigroups generated by automata or given by wreath recursion for GAP system (joint with Y. Muntyan). Accepted Package. Last release: 9/30/2019 (version 1.3.2)
• Script related to the classification of groups generated by 3-state automata over 2-letter alphabet

Edited Volumes

• 24th International Conference, DLT 2020, Tampa, FL, USA, May 11–15, 2020, Proceedings. Editors: Nataљa Jonoska and Dmytro Savchuk, Lecture Notes in Computer Science book series (LNCS, volume 12086), Springer
• Special Issue: Developments in Language Theory 2020, Editors: Nataљa Jonoska and Dmytro Savchuk, International Journal of Foundations of Computer Science, V.32 (2021), no.6

Reports

• "Essentially Free Actions of Self-similar Groups" (with R. Grigorchuk), Scientific Bulletin of Chernivtsi University, 2012, V.2, #2-3, 53-58
• "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), Scientific Bulletin of Chernivtsi University 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.

Updated: August 27th, 2024