8:30–9:00: Registration

9:00–9:30: Opening

9:30–10:00: Lecture

Czesław Ryll-Nardzewski - mathematician with great personality
Michał Morayne, Wrocław University of Science and Technology

10:00–10:50: Lecture of the Winner of the Ryll-Nardzewski Prize

Impossibility results in dynamical systems
Marcin Sabok (McGill University)

10:50–11:40: Lecture of the Winner of the Early Career Ryll-Nardzewski Prize

Ultrafilters and Ramsey theory
Serhii Bardyla (University of Vienna)

11:40–12:10: Coffee and snacks

12:10–13:00: Lecture of the Winner of the Chilean National Prize for Exact Sciences

Rigidity problems in the Dynamics of Endomorphisms of Symbolic Dynamical Systems
Alejandro Maass (Universidad de Chile)

13:00–13:50: Lecture of the Laureate of the Banach Prize

On the problem of soliton resolution
Jacek Jendrej (AGH University of Kraków)

13:50–14:15: Coffee and snacks

14:15–15:00: Popular science lecture

Mathematical discovery in the age of AI
Bartosz Naskręcki (Adam Mickiewicz University in Poznań)
public streaming: link

15:00–17:00: Reception

17:00–19:00: Break
(the auditorium must be vacated for technical reasons)

19:00–20:30: Artistic coda

GenOM
Performance by artists of Wrocław Opera

Marcin Sabok (McGill University)
Impossibility results in dynamical systems

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.

Serhii Bardyla (University of Vienna)
Ultrafilters and Ramsey theory

In this presentation, we explore the interplay between Ramsey theory and ultrafilters. Motivated by the classical Schur theorem, we will introduce Schur ultrafilters, discuss their set-theoretic and combinatorial properties, and demonstrate their application to the automatic continuity of group operations in chart groups. Finally, using ultrafilter methods, we present an extension of the classical Hindman's theorem.

Alejandro Maass (Universidad de Chile)
Rigidity problems in the Dynamics of Endomorphisms of Symbolic Dynamical Systems

Furstenberg asked whether Lebesgue measure is the only ergodic, invariant probability measure on the circle, not supported on a finite set, that is invariant under multiplication by both 2 and 3. Although the problem remains open, important results are known under a positive-entropy assumption. This question has inspired related problems across dynamical systems. In this talk, we focus on symbolic dynamics and study mostly algebraic endomorphisms of subshifts of varying complexity. We will present new questions concerning their classification and discuss the XOR cellular automaton on the full two-symbol shift as a guiding example.

Jacek Jendrej (AGH University of Kraków)
On the problem of soliton resolution

Dispersive partial differential equations are evolution equations (that is, involving the time variable) whose solutions preserve the total energy, but decay in large time due to the fact that various frequencies propagate with distinct velocities. In some cases, there exist special solutions called solitons, which do not change their shape as time passes. The Soliton Resolution Conjecture predicts that solitons are the only obstruction to the decay of solutions: every solution eventually decomposes into a superposition of solitons and a decaying term called radiation. After a general introduction, I will discuss the conjecture in the setting of a geometric wave equation. Based on a joint work with Andrew Lawrie.

Bartosz Naskręcki (Adam Mickiewicz University in Poznań)
Mathematical discovery in the age of AI

The rapid development of large language models over the past few years has led us to experiment with reasoning and recognize the potential usefulness of models in science. I will discuss whether we are actually close to AI surpassing mathematicians and what this means in practical science. We will see how various new techniques, including reasoning token models and multi-agent models, achieve high effectiveness in some types of reasoning, but still fail completely in others. I will try to argue why this is the case and whether the end of scientific institutions is upon us. I will comment also on the latest proliferation of AI generated proofs of mathematical conjectures and the post-AI landscape that emerges from this explosion.

11:15–11:25: opening

Rector of the Wrocław University of Science and Technology
prof. dr hab. inż. Arkadiusz Wójs

11:30–12:25: Ryll-Nardzewski Lecture

Nikos Frantzikinakis
University of Crete
Ergodic properties of bounded sequences and applications

12:30–13:10:

Piotr Biler
University of Wrocław
A nonlocal parabolic problem

13:15–13:55:

Jacek Małecki
Wrocław University of Science and Technology
Stochastic particle systems with weak repulsive forces

Nikos Frantzikinakis (University of Crete)
Ergodic properties of bounded sequences and applications

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.

Piotr Biler (University of Wrocław)
A nonlocal parabolic problem

Jacek Małecki (Wrocław University of Science and Technology)
Stochastic particle systems with weak repulsive forces

The talk will be devoted to stochastic particle models with repulsive interactions, with particular emphasis on cases where the repulsive force coming from a singular drift is too weak to prevent particle collisions. We will discuss conditions ensuring the existence of such models together with an examination of their behavior, focusing on collisions, multi-collisions, and the times of collisions. The presented results will be partially drawn from joint projects with Sergio Andraus, Piotr Graczyk, and Nicole Hufnagel.