Web page of Dmytro Savchuk

home | teaching | research | puzzles | personal

Research interests

Geometric and combinatorial group theory. Geometry of Out(Fn). 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.

Publications and Preprints

  1. "Affine Automorphisms of Rooted Trees" (with S. Sidki), Geometriae Dedicata, 183 (2016), 195213
    (arXiv | journal)
  2. "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), 433457
    (arXiv | journal)
  3. "Ergodic decomposition of group actions on rooted trees" (with R. Grigorchuk), Proceedings of the Steklov Institute of Mathematics, V.292 (2016), Issue 1, 94111
    (arXiv | journal)
  4. "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)
  5. "An Example of an Automatic Graph of Intermediate Growth" (with A. Miasnikov), Annals of Pure and Applied Logic, 166 (2015), no. 10, 10371048
    (arXiv | journal)
  6. "Schreier graphs of actions of Thompson's group F on the unit interval and on the Cantor set", Geometriae Dedicata, V.175 (2015), 355372
    (arXiv | journal)
  7. "Self-similar groups acting essentially freely on the boundary of the binary rooted tree" (with R. Grigorchuk), Contemporary Mathematics, V.611, 2014, 948
    (arXiv | volume)
  8. "On the geometry of the edge splitting complex" (with L. Sabalka), Groups, Geometry, and Dynamics, 8 (2014), no. 2, 565598
    (arXiv | journal)
  9. "On Restricting Subsets of Bases in Relatively Free Groups" (with L. Sabalka), IJAC, V.22 (2012), no.4
    (arXiv)
  10. "Automata generating free products of groups of order 2" (with Y. Vorobets), Journal of Algebra, V.336 (2011), Issue 1, 5366
    (arXiv | journal)
  11. "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)
  12. "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)
  13. "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)
  14. "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)
  15. "The spectral problem, substitutions and iterated monodromy" (with R. Grigorchuk and Z. Sunic), CRM Proceedings and Lecture Notes 42 (2007), 225-248
    (arXiv)
  16. "On Sushchansky p-groups" (with I. Bondarenko), Algebra Discrete Math., 2007, no. 2, 22-42
    (arXiv | journal)
  17. "On word problem in contracting automorphism groups of rooted trees", Bulletin of the University of Kiev, Series: Physics & Mathematics, 2003, #1, 51-56
    (pdf)
  18. "Submanifold Projection" (with L. Sabalka), preprint, 30 pp., 2012
    (arXiv)

Software

Reports

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: September 09th, 2016

home | teaching | research | puzzles | personal