One Day Ergodic Theory Meeting

One Day Ergodic Theory Meeting - Warwick 2026

When: Wednesday 4 November 2026, 13:00-18:00.

Where: , 91影视破解版.

Speakers: Rhiannon Dougall, Francisco Arana-Herrera, Victor Kleptsyn, John Smillie

Schedule:

- 11:50 - 12:45 () : Lunch (we will leave for lunch from the common room of the Zeeman Building at 11:50)

- 13:00 - 14:00 (MS.03): Victor Kleptsyn

Title: Denjoy examples of class C^1 with affine dynamics outside the invariant Cantor set

Abstract: The simplest construction of a Denjoy example (a circle homeomorphism with an irrational rotation number and a Cantor minimal set) in the class of homeomorphisms is to blow up an orbit of a pure rotation map, replacing each of its points with an interval, and to extend the homeomorphism to each of these intervals in an affine way. Though, this construction as is doesn鈥檛 allow to obtain C^1-diffeomorphisms due to the derivatives at the endpoints of the intervals; usually, C^{1+\tau}-Denjoy examples are constructed by Herman鈥檚 construction, where the extension to the intervals is made with the derivatives 1 at the endpoints.

I will start the talk by presenting a recent construction of Andr茅s Navas and myself of Denjoy examples of class C^1, that are nevertheless exactly affine on each of the intervals in the complement to the minimal Cantor set. Then, I will present a modification of this construction by Maximiliano Escayola, that has allowed him to answer in the negative the question, asked by Dusa McDuff 45 years ago : for a Denjoy example of class C^1, it is always true that in the set of logarithms of lengths of the complementary intervals, the gaps tend to zero?

- 14:10 - 15:10 (D1.07): Rhiannon Dougall
Title: Relative tau, Expanders, and decay of correlations for certain expanding maps

Abstract: Expander graphs are characterized as being "highly connected". Another way think about this is: a sequence of k-regular expander graphs have fast mixing for the simple random walk. We see this phenomena in other places: the "geodesic flow" dynamics associated to certain congruence covers of $\mathbb{H}^2/PSL(2,Z)$ have exponential decay of correlations (uniform in the covers), and this can be seen as being related to the expander property for the associated Cayley graphs.

The previous two examples one has some nice structures: self-adjoint operators and representation theory. Does one still expect good mixing behaviour for analogous extensions of maps with 鈥渉yperbolic鈥� behaviour? I will consider this problem for dynamics driven by 1. A subshift of finite type, or 2. An expanding interval map. The problem is (surely?) interesting but the arguments are also nice for how they gather adjacent concepts mathematics.

- 15:10 - 15:45 (Common Room): Break

- 15:45 - 16:45 (D1.07): Francisco Arana-Herrera

Title: Lyapunov Spectra Beyond Coding

Abstract: Many important questions in dynamics can be reduced to the study of positivity or simplicity of Lyapunov exponents of a suitable cocycle over a suitably chaotic base. The most common approach in the literature is via coding, i.e., reduction to random matrix products induced by countable state Markov chains. In this talk we discuss a new approach to this problem that entirely bypasses coding. As a particular case, we apply our results to arbitrary SL(2,R) orbit closures of Abelian differentials, for which coding is not known to hold. This is joint work with DeWitt, Eskin, Gadre, Gutierrez-Romo, Lima, Matheus, Rafi, and Schleimer.

- 16:50 - 17:50 (D1.07): John Smillie

Title: Horospherical measures in invariant subvarieties

Abstract: The study of the horocycle flow on SL(2,R)/SL(2,Z) is a classic topic in dynamics. The space SL(2,R)/SL(2,Z) is an example both of a locally homogeneous space and a moduli space of translation surfaces. Work of Dani, Ratner and others led to a comprehensive theory of dynamics in homogeneous spaces that generalises the classic case above.

Major advances have also been made in understanding analogous dynamical questions in the translation surface setting but the complete picture is not yet clear. I will describe a translation surface analog of Dani鈥檚 theory of horospherical measures which extends results of Lindenstrauss and Mirzakhani. This work is a result of collaborations with F. Ygouf, B. Weiss, P. Smillie and C. Wu.

- 18:30 - : Dinner at Earlsdon (15-20 mins walking from Coventry train station), precise location tba.