Curriculum Vitae
Download CV (PDF)The PDF is a concise two-page version of my CV. You can find more detail below and elsewhere on this site, including abstracts and links for all my papers on the Papers page.
Education
Research visits and internships
Recent publications
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Tranched graphs: consequences for topology and dynamics
Authors: MichaĹ Kowalewski, Piotr Oprocha
Fundamenta Mathematicae 273, no. 1, 1â46 ⢠2026 ⢠doi:10.4064/fm240613-5-12
We compare quasi-graphs and generalized sin(1/x)-type continua, which are two classes of continua that generalize topological graphs and contain the Warsaw circle as a nontrivial common element. We show that neither class is a subset of the other, provide some characterizations, and present illustrative examples. We unify both approaches by considering the class of tranched graphs, compare it to concepts known from the literature, and describe how the topological structure of its elements restricts possible dynamics.
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Every nondegenerate Peano continuum admits a pure mixing selfmap
Authors: KlĂĄra KarĂĄsovĂĄ, MichaĹ Kowalewski, Piotr Oprocha
Proc. Amer. Math. Soc. 154, no. 10, 4389â4403 ⢠2026 ⢠doi:10.1090/proc/17765
We prove that every Peano continuum (a space that is a continuous image of [0,1]) admits a topologically mixing but not exact map. The constructed map has a dense set of periodic points.
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Observable Dynamics and the Generic Coincidence of Milnor, Statistical, and Physical Attractors
Authors: Magdalena ForyĹ-Krawiec, Jana HantĂĄkovĂĄ, MichaĹ Kowalewski, Piotr Oprocha
arXiv:2511.09718 (submitted) ⢠2025
We study observable dynamics of generic continuous interval maps. We prove that, for a residual subset of C([0,1]), the global Milnor, statistical, and physical attractors coincide with the non-wandering set. Thus, for a typical interval map, the asymptotic dynamics detected by Lebesgue-almost every initial condition recovers all recurrent dynamics. The common attractor is a robust Cantor set of zero Hausdorff dimension. Moreover, every invariant probability measure has a basin of zero Lebesgue measure. We also present examples showing that, outside the generic setting, positive topological entropy may occur outside the global Milnor attractor, and the three attractors need not coincide.
Presentations & Talks
1st Hebei International Conference on Dynamical Systems
Poster: âMixing and exact maps of Peano continuaâ â Shijiazhuang, China
2nd ISTA Summer School in Dynamical Systems
Poster: âMixing and exact maps of Peano continuaâ â Strobl, Austria
New Challenges in Celestial Mechanics
Talk: âObservable dynamics and the generic coincidence of Milnor, statistical and physical attractorsâ â Cetraro, Italy
9th OstravaâPrague Seminar on Topology & Dynamics
Talk: âMixing and exact maps of Peano continuaâ â Ostrava, Czech Republic
Special Session on Continuous and Complex Dynamics, AMS Sectional Meeting
Talk: âDynamics of tranched graph mapsâ â Online
Topological, Analytic, Algebraic and Geometric methods in the dynamics of differential equations and homeomorphisms on manifolds, and related topics
Talk: âTranched graphs: consequences for topology and dynamicsâ â Shanghai, China
The 2nd Maribor Mini Workshop on Topological Dynamics, Continuum Theory, and related topics
Talk: âConnections between tranched graphs and Class Wâ â Maribor, Slovenia
From Topology to computations in dynamical systems
Poster: âGraphs with tranchesâ â KrakĂłw, Poland
The 38th Summer Conference on Topology and its Applications
Talk: âGraphs with tranchesâ â Coimbra, Portugal
The 1st Maribor Mini Workshop on Topological Dynamics, Continuum Theory, and related topics
Talk: âTopological properties of tranched graphsâ â Maribor, Slovenia
Conference on Generic Structures
Talk: âTopological properties of tranched graphsâ â BÄdlewo, Poland
Conferences, Workshops & Schools Attended
Simons Semester: Continued Fractions, Fractals, Ergodic theory and Dynamics
â Warsaw, Poland
Simons Semester: Invariant Structures in Groups, Spaces, and Algebras
â Warsaw & BÄdlewo, Poland
Beyond Uniform Hyperbolicity
â Trieste, Italy
School and Workshop in Dynamical Systems
â Trieste, Italy
Discrete Mathematics and Computer Science
â Marseille, France
Big Ideas in Dynamics
â remote
Spanish+Polish Mathematical Meeting
â ĹĂłdĹş, Poland
Simons Semester: Topological, smooth and holomorphic dynamics, ergodic theory, fractals
â Warsaw & BÄdlewo, Poland
Big Ideas in Dynamics
â remote
Teaching
Dynamical Systems by Example
Problem-solving classes (10h) and Python computer labs (20h), 2 groups, in English â AGH University of Krakow
Topological Dynamics and Chaos
Problem-solving classes (30h), in Polish â AGH University of Krakow
Topology
Problem-solving classes (30h), in Polish â AGH University of Krakow
Languages & Skills
Polish (native speaker), English (ACERT C1 certificate)
Python, LaTeX