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.

Currently, I'm the principal investigator of the POLS project DynComp which is running from 2021 to 2023 and is 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).

Publications

Peer-reviewed research articles

Amorphic complexity of group actions with applications to quasicrystals

with G. Fuhrmann, T. Jäger and D. Kwietniak, Trans. Am. Math. Soc., accepted for publication

The structure of mean equicontinuous group actions

with G. Fuhrmann and D. Lenz, Israel J. Math. 247:75-123 (2022)

Thermodynamic formalism for transient dynamics on the real line

with M. Keßeböhmer and J. Jaerisch, Nonlinearity 35(2):1093-1118 (2022)

The bifurcation set as a topological invariant for one-dimensional dynamics

with G. Fuhrmann and A. Passeggi, Nonlinearity 34(3):1366-1388 (2021)

Measures and stabilizers of group Cantor actions

with O. Lukina, Discrete Contin. Dyn. Syst. - A 41(5):2001-2029 (2021)

Constant length substitutions, iterated function systems and amorphic complexity

with G. Fuhrmann, Math. Z. 295:1385-1404 (2020)

A classification of aperiodic order via spectral metrics & Jarnìk sets

with M. Keßeböhmer, A. Mosbach, T. Samuel and M. Steffens, Ergodic Theory Dyn. Syst. 39(11):3031-3065 (2019)

Hyperbolic graphs: critical regularity and box dimension

with L. Díaz, K. Gelfert and T. Jäger, Trans. Am. Math. Soc. 371:8535-8585 (2019)

Non-smooth saddle-node bifurcations II: dimensions of strange attractors

with G. Fuhrmann and T. Jäger, Ergodic Theory Dyn. Syst. 38(8):2989-3011 (2018)

Some remarks on modified power entropy

with T. Jäger, Dynamics and Numbers, Contemp. Math. 669:105-122 (2016)

Amorphic complexity

with G. Fuhrmann and T. Jäger, Nonlinearity 29(2):528-565 (2016)

Coupled skinny baker's maps and the Kaplan-Yorke conjecture

with B. Hunt, Nonlinearity 26(9):2641-2667 (2013)

Dimensions of attractors in pinched skew products

with T. Jäger, Commun. Math. Phys. 320(1):101-119 (2013)

Scientific activities

Kraków's Recurrence 2022 - kick-off meeting JU Dynamical Systems Seminar

organized with P. Kunde and D. Kwietniak (30 September-1 October 2022, Kraków, Poland, webpage)

Thermodynamic formalism - Applications to geometry and number theory - in memory of Bernd O. Stratmann

organized with K. Falk, T. Samuel, M. Keßeböhmer, S. Munday and S. Kombrink (10-12 July 2017, Bremen, Germany)

Workshop on Fractals, Dynamics and Quasicrystals

organized with K. Gelfert and T. Jäger (5-9 October 2015, Wöltingerode, Germany, webpage)

1st Bremen Winter School on Multifractals and Number Theory

organized with T. Samuel (18-22 March 2013, Bremen, Germany, webpage)

Workshop on Skew Product Dynamics and Multifractal Analysis

organized with T. Jäger (1-5 October 2012, Luisenthal, Germany, webpage)

Teaching

Ergodic Theory I

teaching assistant for problem class (Jagiellonian University, winter term 2020/2021)

Smooth Dynamical Systems

teaching assistant for problem class (Jagiellonian University, winter term 2020/2021)

Use of English in Mathematics

group leader of 2 seminars (Jagiellonian University, winter term 2020/2021)

Ergodentheorie II

lecturer together with R. Zweimüller (University of Vienna, summer term 2019)

Analysis 3

teaching assistant for 2 problem classes (University of Bremen, winter term 2011/2012)

DynComp

The POLS project Dynamical complexity and pseudometrics (DynComp) is running from 2021 to 2023 and is funded by the Norway Grants via the National Science Center (NCN) of Poland. The webpage of the project can be found here.

Scope of the project

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.

Contact

Address

Faculty of Mathematics and Computer Science
Jagiellonian University
ul. Prof. S. Łojasiewicza 6
30-348 Kraków, Poland

Office

Room 2012

Phone

+48 12 664 76 39

Email

maik.groeger@im.uj.edu.pl