2025-26

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. Everybody is welcome.

Term 2

13.01.2026: Michael Baake (Bielefeld)

Title: On the long-range order induced by the Hat and Spectre monotiles

Abstract: Hat and Spectre are recently discovered aperiodic monotiles for the Euclidean plane. Each of them gives rise to a class of tiling dynamical systems under the translation action of $\mathbb{R}^2$. Combining methods from algebraic topology, dynamical systems theory and harmonic analysis, we show that they have pure-point spectrum and display quasiperiodic long-range order. In fact, both tilings are reprojections of self-similar tilings with a 4D embedding space, and as such rather different from the limit-periodic structure of the Taylor--Socolar monotile. (This is joint work with Franz Gähler and Lorenzo Sadun).

20.01.2026: Daniel Monclair (Paris-Saclay)

Title: Spectra of anti-de Sitter quasi-Fuchsian manifolds

Abstract: Two spectral theories arise from the study of hyperbolic manifolds: the Laplacian, and the geodesic flow (Ruelle-Pollicott resonances). There are many results building explicit bridges between these two spectra. For Lorentzian manifolds, the elliptic Laplacian is replaced with a hyperbolic operator, leading to a completely different spectral theory. We will see that we can still connect this operator with the geodesic flow for some 3-dimensional anti-de Sitter (i.e. Lorentzian with constant negative curvature) manifolds.

Based on joint work with B. Delarue and C. Guillarmou.

27.01.2026: Didac Martinez (Luxembourg)

Title: A geometric correspondence for flow reparameterizations of a hyperbolic group

Abstract: We study continuous reparameterizations of the Mineyev flow associated to hyperbolic groups. We construct a correspondence between reparameterizations and a natural space of hyperbolic potentials, extending classical results for Hölder time changes. In particular, symmetric reparameterizations are in bijection with the metric completion of the space of Gromov hyperbolic metrics. A key ingredient in the proof is the density of Green metrics in this space. We further establish continuity of the Bowen–Margulis map and convergence of normalized counting measures over closed geodesics toward the associated geodesic current. These results provide a unified framework linking reparameterizations, Gromov hyperbolic metrics, and geodesic currents. This is work in progress with Stephen Cantrell and Eduardo Reyes.

03.02.2026: Rigoberto Zelada (Warwick)

Title: Coexistence of mixing and rigid behaviors of probability preserving transformations

Abstract: We will define and discuss the concept of \textit{group of rigidity} (associated with a collection of finitely many sequences). As we will see, groups of rigidity play an instrumental role in answering questions stemming from the theory of generic Lebesgue preserving automorphisms of $[0,1]$, IP-ergodic theory, multiple recurrence, and spectral theory. A simple statement which epitomizes the type of results that one can obtain with the help of groups of rigidity is the following: For any $(b_1,...,b_\ell)\in \mathbb N^\ell$ one has that there is no vector $(a_1,...,a_\ell)\in \mathbb Z^\ell$ orthogonal to $(b_1,...,b_\ell)$ with some $|a_j|=1$ if and only if there is an increasing sequence $(n_k)_{k\in \mathbb N}$ in $\mathbb N$ with the property that for every $F\subseteq \{1,...,\ell\}$ there is a $\mu$-preserving transformation $T_F:[0,1]\rightarrow [0,1]$ ($\mu$ denotes the Lebesgue measure) such that

$ \lim_{k\rightarrow\infty}\mu(A\cap T_F^{-b_jn_k}B)=\mu(A\cap B),\,\text{ if }j\in F$ and $=\mu(A)\mu(B),\,\text{ if }j\not\in F$ for every pair of measurable sets $A,B\subseteq [0,1]$. Part of this talk is based on joint work with Vitaly Bergelson.

10.02.2026: Will Hide (Oxford)

17.02.2026: Rodolphe Richard (Manchester)

24.02.2026: Timothée Bénard (CNRS)

Title: Random walks on homogeneous spaces -- Followed on by lectures series on

Effective equidistribution of random walks on the torus

Abstract: I will explain why a random walk on a simple homogeneous space equidistributes toward the Haar measure with an explicit rate, provided the walk is not trapped in a finite invariant set and the driving measure is Zariski-dense with algebraic coefficients. The argument is based on a multislicing theorem which extends Bourgain's projection theorem and presents independent interest. Joint work with Weikun He.

03.03.2026: Tobias Hartnick (Karlsruhe)

10.03.2026: Victor Kleptysn (CNRS)

17.03.2026:

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 with Liyang Shao(University of California, Berkeley).

Subhajit Jana

Title: 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)

Title: Recent results on dynamical Diophantine approximation

Abstract: Historically metric Diophantine approximation consists, in studying the size of sets approximable at a certain speed by rational numbers. Many very natural analogs have been considered and studied. Among such analogs, given an ergodic system (T,m) and x, a m-typical point, the dimension of point approximable at a given rate by the orbit (T^n(x)) has been a topic of interest the last 15 years . This problem was originally introduced by Fan Shmeling and Troubetzkoy for T the doubling of the angle and has known many generalizations since. I will talk about two of them, one generalizes directly the result mentioned, the other considers dynamical approximation by rectangles. This talk will be based on the following two articles:

-Hausdorff dimension of dynamical Diophantine approximation associated with ergodic mixing systems, Adv. Math, 2025

-Random covering by rectangles on self-similar carpets, arXiv:2510.04879

09.12.2025: William Hide (Oxford)

Title: Spectral gaps of random hyperbolic surfaces

Abstract: Based on joint work with Davide Macera and Joe Thomas. The first non-zero eigenvalue, or spectral gap, of the Laplacian on a closed hyperbolic surface encodes important geometric and dynamical information about the surface. We study the size of the spectral gap for random large genus hyperbolic surfaces sampled according to the Weil-Petersson probability measure. We show that there is a c>0 such that a random surface of genus g has spectral gap at least 1/4-O(g^-c) with high probability. Our approach adapts the polynomial method for the strong convergence of random matrices, introduced by Chen, Garza-Vargas, Tropp and van Handel, and its generalization to the strong convergence of surface groups by Magee, Puder and van Handel, to the Laplacian on Weil-Petersson random hyperbolic surfaces.