Central European Mathematical Research Lab is one of the flagship projects created during the implementation of the "Excellence Initiative - Research University" programme at Jagiellonian University.

The CENMATRE operates within the Faculty of Mathematics and  Computer Science of the Jagiellonian University and its research activities encompass a range of areas, especially dynamical systems theory, ergodic theory, and their interactions with other fields such as number theory and probability.

The head of the project is Adam Kanigowski. CENMATRE closely collaborates with the dynamical systems group at Jagiellonian University and will collaborate with the Dioscuri Centre: Random Walks in Geometry and Topology (PI: Mikołaj Frączyk). The Dioscuri Centre is to begin operations in September 2023

Currently, we investigate the chaotic properties of dynamical systems. We are interested in dynamical systems with positive entropy as well as those with zero entropy. In the positive entropy case, we try to understand interactions between ergodic and statistical properties such as the relations between Bernoullicity or the $K$-property and rates of mixing or limit theorems. For systems of zero entropy, which is often the condition defining nonchaotic behaviour, we study appearance of the mixing and higher order mixing properties, orbit distribution, and joinings. Among zero-entropy dynamical systems, we focus mostly on the class of parabolic ones, i.e. systems for which the orbit growth is polynomial in time.

Recently, we also study the so-called {\em sparse} ergodic theorems, i.e., we study the behaviour of orbits sampled along a small but arithmetically rich subset of the natural numbers (such as primes). This part of the activity naturally involves studying interactions between smooth dynamical systems and number theory. We also study some equivalence relations in abstract ergodic theory such as isomorphism and Kakutani equivalence.