Ergodic Theory and Dynamical Systems Seminar

Warwick ETDS Seminar 2025-2026

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.

Term 1

Organizers: Tom Rush, Cagri Sert, Han Yu

07.10.2025: Demi Allen (Exeter)

Title: Rectangular shrinking targets for self-similar carpets

Abstract: Suppose $(B_i)_{i \in \mathbb{N} }$ is a sequence of (shrinking) balls in some ambient space $X$ and we are interested in the set of points $x \in X$ such that $x \in B_i$ for infinitely many $i \in \mathbb{N}$. This is a \emph{shrinking target set}. The terminology of ``shrinking targets'' was first introduced by Hill and Velani in 1995. Since then, shrinking target problems have received a great deal of interest, especially with regards to studying the measure-theoretic and dimension-theoretic properties of shrinking target sets. In this talk, I will discuss some recent work with Thomas Jordan (Bristol, UK) and Ben Ward (York, UK) where we establish the Hausdorff dimension of a shrinking target set where our "targets'' are rectangles, as opposed to balls, and our ambient space is a self-similar carpet.

14.10.2025: Jose Alves (Porto)

Title: Linear response for skew-product maps with contracting fibres

Abstract: We study solenoids with a base given by a family of intermittent circle maps. By employing an averaged, balanced fixed-point equation for a measurable family of fibre conditionals – constructed via a reverse Markov kernel of the base dynamics relative to its physical measure – we establish the existence and parameter differentiability of the fibre family in an appropriate Banach space. Furthermore, we derive a split linear-response formula, separating a fibre term (controlled by uniform contraction) from a base term. This is ongoing work in collaboration with Wael Bahsoun.

21.10.2025: Ian Short (Open University)

Title: Iterated function systems on hyperbolic Riemann surface

Abstract: A classical result known as the Denjoy–Wolff theorem describes the dynamics of the iterates of a holomorphic self-map of the unit disc, and this theorem was generalised by Heins to all hyperbolic Riemann surfaces. Here we consider results of this type for left and right iterated function systems of holomorphic maps. We explore the geometric differences between these two types of systems and, using hyperbolic derivatives and topological arguments, we recover and improve on several recent results in holomorphic dynamics. This is joint work with Marco Abate.

27.10.2025 (Special date, Special event). Dynamic Afternoon at Warwick

04.11.2025: Anders Karlsson (Geneva)

Title: An isometry fixed-point theorem and applications to bounded linear operators

Abstract: I will present a fixed-point theorem stating that every isometry of a metric space admits a fixed-point in the metric compactification of the injective hull of the space. When the metric space has a conical bicombing—as is the case for convex subsets of Banach spaces, CAT(0) spaces, injective spaces, or spaces of positive operators—the injective hull is not needed. As a consequence, it yields a generalization of the von Neumann mean ergodic theorem from Hilbert spaces to arbitrary Banach spaces, in contrast to the usual mean ergodic formulation which is known to fail in general. Another corollary asserts that every invertible bounded linear operator admits an invariant metric functional on the space of positive operators. There are also consequences for biholomorphisms and diffeomorphisms.

11.11.2025: Jonathan Chapman (Warwick)

Title: Recurrence properties of polynomial sumsets

Abstract: A famous question of Katznelson asks whether the notion of topological recurrence for arbitrary topological dynamical systems can be understood by only considering rotation systems on finite-dimensional tori. One of the many equivalent forms of this problem concerns showing that any finite colouring of the integers produces a monochromatic set C such that the difference set C - C contains a Bohr set, which is an entire set of return times for a finite-dimensional toral rotation system. In this talk, I will discuss recent results on finding Bohr sets in other linear combinations of sets, such as A - A + C, where C is a monochromatic set and A is an arbitrary set of integers with positive upper density. I will also show how transference techniques from additive combinatorics can be used to find Bohr sets inside linear combinations of monochromatic and relatively dense subsets of arithmetically interesting sequences of integers, such as the squares or shifted prime numbers.

18.11.2025: Shreyasi Datta and Subhajit Jana (York and QMUL)

Shreyasi Datta

Title: Inhomogeneous bad is winning and null.

Abstract: We will introduce the notion of weighted badly approximable vectors, and its inhomogeneous analogue. The set of badly approximable vectors correspond to bounded orbits under some diagonal flow in a certain homogeneous space. We discuss that this set can be very large (winning) in a sense and in some other sense it is very small (measure wise). We show a combination of tools from homogeneous dynamics tools and soft analysis to deal with the inhomogeneous case. This is a joint work withLiyang ShaoLink opens in a new window(University of California, Berkeley).

Subhajit Jana

Optimal Diophantine exponent and density hypothesis

Abstract: We talk about the intrinsic Diophantine exponent in the set-up of Z[1/p]-points of SL(n) approximating the real points of the same and Sarnak's density hypothesis in relevance to this. A recent joint work with Edgar Assing.

25.11.2025: Richard Sharp (Warwick)

Titles: Equidistribution in amenable skew products

Abstract: We will discuss the distribution of periodic points in amenable skew product extensions of countable state Markov shifts and its relation to Gurevich pressure.

02.12.2025: Edouard Daviaud (Liege)

09.12.2025: William Hide (Oxford)

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Contact:
Mathematics Research Centre
Zeeman Building
University of Warwick
Coventry CV4 7AL - UK
E-mail:
MRC@warwick.ac.uk