The fourth CRN Lecture will take place on September 9, 2026 as a part of the Ryll-Nardzewski Day at the Chilean-Polish Mathematical Meeting. Our speaker is the laurate of the Ryll-Nardzewski Prize,

Prof. Marcin Sabok (McGill University)

who will give a talk

Impossibility results in dynamical systems

Abstract of the talk:

The goal of this talk will be to explain the general framework of anti-classification theorems, which can provide impossibility results for problems in dynamical systems. For example, we will see how phenomena like ergodicity lead to results on non-classifiability by concrete invariants. Then we will discuss stronger phenomena which are connected with probability measure preserving actions of the free groups. At the end I will also mention recent results concerning classification of symbolic systems with the specification property. In particular, we will discuss Problem 32 of Rufus Bowen asking for a classification of symbolic systems with the specification property.

This will be based on recent work with Konrad Deka, Dominik Kwietniak and Bo Peng. The talk will be accessible to non-specialists.

The third CRN Lecture will take place on June 28, 2025 as a part of the Ryll-Nardzewski Day conference starting at 11:15. Our speaker is

Prof. Nikos Frantzikinakis (University of Crete)

who will give a talk

Ergodic properties of bounded sequences and applications

Abstract of the talk:

How can we measure and exploit randomness properties of a bounded sequence? A construction due to Furstenberg from the 70’s allows us to encode the statistical properties of bounded sequences dynamically using the language of ergodic theory. This provides a different point of view, which has important advantages and has led to several breakthroughs in ergodic theory, combinatorics and, more recently, number theory. Examples include various refinements of Szemeredi’s theorem on arithmetic progressions, progress towards the Sarnak and Chowla conjecture, and the partition regularity of Pythagorean triples. I will review some related results with an emphasis on more recent developments.

The second CRN Lecture will take place on June 1, 2024 at 11:45–12:45 in room 1.27, blgd. C-13, as a part of the 2^nd Wrocław Logic Conference. Our speaker is

Prof. Jan van Mill (University of Amsterdam)

who will give a talk

On the modal logic of certain Čech–Stone compactifications

Abstract of the talk:

We discuss topological results that determine the modal logics of ω*, βω and β(ω²). (Here ω² is the ordinal ω², hence topologically it is a discrete union of countably many nontrivial convergent sequences.) For ω* and βω these are known ZFC results. The new result is for β(ω²) and partially answers a question of Shehtman. Its proof relies on Parovičenko’s characterization of ω* under the Continuum Hypothesis.

The first CRN Lecture will take place on June 12, 2023 as a part of the Ryll-Nardzewski Day conference starting at 13:15. Our speaker is

Prof. Vitaly Bergelson (Ohio State University)

who will give a talk

The Prime Number Theorem via Ergodic Theory