Dr Maik Gröger

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
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