About
I'm an assistant professor at the Institute of Mathematics of the Jagiellonian University in Kraków. Beforehand, I was a postdoc in the ergodic theory and dynamical systems research groups at the University of Vienna and University of Jena. I did my PhD in the Dynamical Systems and Geometry Research Group at the University of Bremen.
From 2021 to 2023 I was the principal investigator of the POLS project DynComp which was funded by the Norway Grants via the National Science Center (NCN) of Poland. In the past, my research was also funded by the grant GR 4899/1-1 from the German Research Foundation (DFG).
A central goal of topological dynamics and ergodic theory is the classification of dynamical systems up
to an appropriate notion of isomorphisms. Dynamically defined pseudometrics turn out to be an essential
tool to achieve this task. Moreover, they can induce interesting dynamical invariants reflecting
certain long-term behavior and complexity of a system.
The aim of this project is to extend our understanding of dynamically defined pseudometrics for
continuous actions of topological groups and to examine the corresponding complexity notions which
they induce. Hereby, we are particularly interested in systems exhibiting low complexity
behaviour (in the sense that they have zero entropy whenever the acting group allows for
establishing a reasonable entropy theory).
Prominent examples belonging to this class are systems which are defined by finitely many local rules and
point set dynamical systems associated to regular model sets.
Here, primary examples come from the theory of aperiodic order which provide mathematical models for
quasicrystals.
