Ergodic Theory and Dynamical Systems Seminar

Warwick ETDS Seminar 2026-2027

The seminars are held on Tuesdays at 14:00 in B3.02.

On seminar days we meet for lunch at 12:30 and tea at 15:00 in the common room. Everybody is welcome.

Term 1

Organizers: Jonathan Chapman , Cagri Sert , Rigoberto Zelada

06.10.2026: Matt Bowen (Warwick)

Title: Measurable matchings in Borel group actions

Abstract: We discuss the existence and applications of measurable perfect matchings in graphs defined via Borel actions of finitely generated groups on Borel probability spaces. For instance, we completely characterize amenable groups whose bipartite Schreier graphs admit measurable perfect matchings. As an application we prove that the unit circle can be partitioned into finitely many measurable pieces which can be translated to obtain a copy of the unit area circle, obtaining a new proof and generalizations of Grabowski, Mathe and Pikhurko's measurable circle squaring.

This is based on previous and upcoming work with Kun and Sabok.

13.10.2026: Zhe Wang (Dalian University of Technology, long-term visitor at Warwick)

Title: Quenched invariance principles with rates for random dynamical systems

Abstract: In this talk, we present the Wassertein convergence rate in the quenched invariance principle for random Young towers. We apply the results to a class of random dynamical systems that admit random Young towers, such as i.i.d. translations of intermittent maps.

20.10.2026: Borys Kuca (Jagiellonian University)

Title: Structure of 2-step nilpotent ergodic averages.

Abstract: Multiple ergodic averages play a central role in transferring results from ergodic theory to combinatorics and number theory. Of particular interest are averages with polynomial iterates that arise in the polynomial Szemerédi theorem and its extensions. Their norm convergence was established by Walsh 15 years ago, but his method gave virtually no information on the structure of the limits. Building on recent advances in the abelian setting, I will describe new limiting formulas for polynomial averages induced by 2-step nilpotent measure-preserving actions. I will also present new (positive and negative) results on the joint ergodicity conjecture and introduce various open problems. The talk is based on joint work with Andreas Koutsogiannis and Wenbo Sun

27.10.2026: Alexander Veselov (Loughborough)

Title: Quantum numbers and braid group actions

Abstract: Few years ago, Sophie Morier-Genoud and Valentin Ovsienko introduced a remarkable quantization of the rational numbers as certain rational functions of the deformation parameter q. It turned out that the corresponding singular set, consisting of poles of all such functions, plays an important role in the theory of the braid group B_3, providing an answer to the faithfulness problem for the corresponding specialised Burau representation. I will discuss this link and, if time permits, other important actions of B_3 appeared in number theory and geometry, including some dynamical aspects of these actions. The talk is based on joint works with S. Morier-Genoud, V. Ovsienko, S. Evans and B. Winn.

03.11.2026: (No Seminar) - One Day Ergodic Theory Meeting the next day at Warwick

10.11.2026: Davide Sclosa (King’s College)

Title: Multidimensional Szemerédi Theorem for Pairwise Independent Jointly Intersective Polynomials

Abstract: In joint work with Nikos Frantzikinakis, we develop a new approach to the Joint Intersectivity Conjecture of Bergelson, Leibman, and Lesigne for commuting transformations. The conjecture asserts that the necessary divisibility condition is the only obstruction to polynomial multiple recurrence and, consequently, to the multidimensional polynomial Szemerédi's theorem. We establish the conjecture for pairwise independent polynomials, obtaining the first general result for sequences of arbitrary length beyond the classical one-transformation setting. The main novelty is the development of new techniques that allow to bypass the use of the polynomial Van der Waerden's theorem.

17.11.2026:

24.11.2026: Oliver Jenkinson (Queen Mary)

01.12.2026:

08.12.2026: Vadim Kaimanovich (Rennes)