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I am an Assistant Professor at the Faculty of Applied Mathematics of AGH University of Kraków, Poland. Previously, I was an Assistant Professor at the Institute of Mathematics of the Polish Academy of Sciences (IMPAN) in Wrocław, Poland, and a Senior Research Fellow in the Mathematical Division of the B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine in Kharkiv, Ukraine.
I obtained my undergraduate degree from V. N. Karazin Kharkiv National University in 2009 and completed my PhD at the B. Verkin Institute for Low Temperature Physics and Engineering in 2013 under the supervision of Sergii Bezuglyi. From 2015 to 2017, I was a postdoctoral researcher with Tomasz Downarowicz in IMPAN, Wrocław.
My research interests include ergodic theory and topological dynamics, with a focus on Cantor and Borel dynamical systems. From 2020 to 2024, I was the Principal Investigator of the NCN Sonata grant “Cantor Dynamical Systems and Their Classification.”
Publications
Publications
Preprints
Isomoprhism of generalized Bratteli diagrams, arXiv:2605.18278.
Subdiagrams and invariant measures for generalized Bratteli diagrams, with. S. Bezuglyi, P. Jorgensen, T. Raszeja, and S. Sanadhya, arXiv:2602.19394.
Publications
Inverse limit method for generalized Bratteli diagrams and invariant measures, with. S. Bezuglyi, J. Kwiatkowski, and M. Wata, to appear in Dissertationes Mathematicae, arXiv:2404.14654.
Bratteli diagrams in Borel dynamics, with. S. Bezuglyi, P. Jorgensen, and S. Sanadhya, Groups, Geometry, and Dynamics 20 (2026), 797-869, journal, arXiv:2212.13803.
Measures and dynamics on Pascal-Bratteli diagrams, with S. Bezuglyi, and A. Dudko, J. Math. Phys. Anal. Geom. 22 (2026), 3–21, journal, arXiv:2411.06280.
Rigidity and Toeplitz systems, with H. Bruin, P. Oprocha, and S. Radinger, Forum Mathematicum 38 (2026), 863-892, arXiv:2502.00917.
Horizontally stationary generalized Bratteli diagrams, with S. Bezuglyi, P. Jorgensen, and J. Kwiatkowski, Fund. Math. 271 (2025), 195-225, arXiv:2409.10084.
Invariant measures for reducible generalized Bratteli diagrams, with. S. Bezuglyi and J. Kwiatkowski, J. Math. Phys. Anal. Geom. 20 (2024), 3 – 24, journal, arXiv:2402.17046.
Invariant measures for Cantor dynamical systems, with S. Bezuglyi, Contemp. Math. 744 (2020), 259 – 295, arXiv:1904.09666.
Exact number of ergodic invariant measures for Bratteli diagrams, with. S. Bezuglyi and J. Kwiatkowski, J. Math. Anal. Appl. 480 (2019), 1 – 49, arXiv:1709.00055.
Decisive Bratteli-Vershik models, with T. Downarowicz, Studia Math. 247 (2019), 251 – 271, arXiv:1704.04447.
Dynamics in dimension zero. A survey, with T. Downarowicz, Discrete Contin. Dyn. Syst. 38 (2018), 1033 – 1062, arXiv:1610.02727.
Subdiagrams and invariant measures on Bratteli diagrams, with M. Adamska, S. Bezuglyi and J. Kwiatkowski, Ergodic Theory Dynam. Syst. 37 (2017), 2417 –2452, arXiv:1502.05690.
Bratteli diagrams: structure, measures, dynamics, with S. Bezuglyi, Contemp. Math. 669 (2016), 1 – 36, arXiv:1503.03360.
Invariant measures on Bratteli diagrams (in Ukrainian), Visn. Nac. Akad. Nauk Ukr. 2015(9), 80 – 85, journal.
Subdiagrams of Bratteli diagrams supporting finite invariant measures, with S. Bezuglyi and J. Kwiatkowski, J. Math. Phys. Anal. Geom. 11 (2015), 3 – 17, arXiv:1311.3266.
Orbit equivalent substitution dynamical systems and complexity, with S. Bezuglyi, Proc. Amer. Math. Soc. 142 (2014), 4155 – 4169, arXiv:1201.1622.
Good Measures on Locally Compact Cantor Sets, J. Math. Phys. Anal. Geom. 8 (2012), no. 3, 260 – 279, journal, arXiv:1204.0027.
Infinite measures on Cantor spaces, J. Difference Equ. Appl. 18(2012), 703 – 720, arXiv:1102.1072.
Homeomorphic measures on stationary Bratteli diagrams, with S. Bezuglyi, J. Funct. Anal. 261(2011), 3519 – 3548, arXiv:1008.0850.
Conferences
Conferences
Service
Member of the Organizing Committee for
Conference “Ergodic group actions and unitary representations III”, Warsaw (Poland), 2 - 6 February 2026.
Conference “Ergodic group actions and unitary representations II”, Będlewo (Poland), 15 - 19 June 2025.
Conference “Ergodic group actions and unitary representations”, Warsaw (Poland), 16 - 20 June 2024.
School and conference “Beyond Uniform Hyperbolicity”, Będlewo (Poland), 23 April - 5 May 2023.
Member of the Program Committee for
International Conference of Young Mathematicians dedicated to the 100th Anniversary of Yu. O. Mytropolskiy, Kyiv (Ukraine), 7-10 June 2017.
International Conference of Young Mathematicians, Kyiv (Ukraine), 3-6 June 2015.
Plenary and invited talks
The 2026 Great Plains Operator Theory Symposium, Iowa City, IA (USA), 26–30 May 2026.
Plenary talk: Bratteli diagrams in Cantor and Borel dynamics.
First Dynamical Systems Summer Meeting, Będlewo & Online (Poland), 16–20 August 2021.
Invited talk: Tail invariant measures on Bratteli diagrams and their generalizations.
Algebraic and Combinatorial Invariants of Subshifts and Tillings, a hybrid conference, CIRM, Marseille (France), 11-15 January 2021.
Invited talk: Tail invariant measures on Bratteli diagrams and their generalizations.
7 Forum of Polish Mathematicians with the Participation of Ukrainian Mathematicians, Olsztyn (Poland), 12-17 September 2016.
Invited talk: Bratteli diagrams: structure, measures, dynamics.
The meeting of Presidium of NAS of Ukraine, Kyiv (Ukraine), 17 June 2015.
Invited talk: Invariant measures on Bratteli diagrams.
Selected conferences
The 11th Visegrad Conference on Dynamical Systems, Banská Bystrica (Slovakia), 10 – 12 June 2025.
Dynamics on zero-dimensional spaces: new connections, Leiden (Netherlands), 13 – 17 May 2024.
Dynamics of (Semi-)Group Actions, Łódź (Poland), 26–28 June 2023.
56th Spring Topology and Dynamical Systems Conference, Memphis, TN (USA) & Online, 15 – 18 March 2023.
36th Summer Topology Conference, Vienna (Austria), 18 –22 July 2022.
Czech-Slovak Workshop on Discrete Dynamical Systems, Opava (Czech Republic), 27–30 June 2022.
55th Spring Topology and Dynamical Systems Conference, Waco, TX (USA) & Online, 9–12 March 2022.
Dynamics, Equations and Applications (DEA 2019), Kraków (Poland), 16 – 20 September 2019.
Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Kraków (Poland), 3–7 September 2019.
7th Miniworkshop on Operator Theoretic Aspects of Ergodic Theory, Kiel (Germany), 9–10 November 2018.
Summer School in Dynamics (advanced), ICTP, Trieste (Italy), 23–27 July 2018.
6th Pingree Park Dynamics Workshop, Denver, CO (USA), 17–20 July 2017.
Ergodic Theory Workshop, Chapel Hill, NC (USA), 20–23 April 2017.
Wandering Seminar: A mini-conference on Ergodic Theory and Dynamical Systems, Wrocław (Poland), 2-5 March 2017.
New Advances in Symbolic Dynamics (CNRS Thematic School), Marseille (France), 30 January –3 February 2017.
Applications of Ergodic Theory in Number Theory, Marseille (France), 17-21 October 2016.
Transversal Aspects of Tilings, Oleron (France), 30 May - 24 June 2016.
Wandering Seminar: A mini-conference on Ergodic Theory and Dynamical Systems, Warsaw (Poland), 1-3 April 2016.
Ergodic Theory of Dynamical Systems, Będlewo (Poland), 22-28 November 2015.
International Conference ``Dynamical Systems and their Applications'', Kyiv (Ukraine), 22-26 June 2015.
Wandering Seminar: A mini-conference on Ergodic Theory and Dynamical Systems, Krakow (Poland), 20-23 November 2014.
Activity ``Dynamics and Numbers'', Bonn (Germany), 1 June – 31 July 2014.
Ergodic Theory and Dynamical Systems, Toruń (Poland), 12–16 May 2014.
5th Visegrad Conference on Dynamical Systems, Olsztyn (Poland), 2–6 September 2013.
28th Journées Arithmétiques, Grenoble (France), 1-5 July, 2013.
Dynamical Systems Workshop, University of Maryland, College Park, MD (USA), 4–7 April 2013.
Ergodic Theory Workshop, Chapel Hill, NC (USA), 21–24 March 2013.
ICTP-ESF School and Conference in Dynamical Systems, Trieste (Italy), 21 May – 8 June 2012.
Modern Dynamics and its Interaction with Analysis, Geometry and Number Theory, Będlewo (Poland), 27 June – 24 July 2011.
Czech-Slovak-Spanish Workshop on Discrete Dynamical Systems, La Manga del Mar Menor (Spain), 20 –24 September 2010.
Teaching
Teaching
AGH University of Krakow, Poland
• Topology (2025/26 instructor)
• Mathematical Analysis (2022/23 – 2025/26 instructor, 2023/24 - 2025/26 lecturer)
• Mathematical Analysis I (2018/19 – 2025/26 instructor, 2025/26 - lecturer)
• Mathematical Analysis II (2018/19 – 2022/23 instructor)
• Higher Algebra (2022/23 - 2025/26 instructor, 2023/24 - 2025/26 lecturer)
• Algebra (2018/19 – 2022/23 instructor)
• Linear Algebra and Geometry (2025/26 - instructor)
• Algebra and Calculus (2025/26 - instructor)
• Mathematics I (2024/25 - instructor and lecturer)
• Mathematics II (2020/21 - lecturer, 2021/22, 2025/26 - instructor)
Graduate students and postdocs
Graduate students and postdocs
Graduate students
Sejal Babel co-advised with Dominik Kwietniak, Jagiellonian University in Kraków, 2019 – 2026.
Thesis: Invariant measures from the viewpoint of generic points.
Graduated: 2026.
Postdocs
Thiago Costa Raszeja, AGH University of Kraków, 2021 – 2023.
Contact
Contact
Faculty of Applied Mathematics,
AGH University of Krakow,
Al. Mickiewicza 30,
30-059 Krakow, Poland
E-mail: okarpel@agh.edu.pl
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