Dynamics, Number theory and Probability - 11 and 12 Feb 2026

What: The conference is a two day event showing new directions combining ergodic theory and dynamical systems with number theory and probability theory. In order to make the talks more accessible for younger researchers (in particular last year undergraduate students and PhD students) we will give some introductory talks before the start of the conference. 

To attend this two day meeting, there is no registration nor any fee. However, to help us minimize waste and plan effectively for the refreshment break and dinner reservation, we kindly ask anyone planning to attend to consider filling out the following short form. Your participation is entirely optional, but it would be greatly appreciated.

When: Conference: starting Wednesday, 11 Feburary 2026, 1:30pm to Thursday 12 February 2026, 12:30pm
Introductory talks for young researchers: 11 Feburary 2026, 11:00am to 12:30pm

Where: University of Exeter, Streatham Campus, for rooms and precise times see schedule below.

Speakers:
Bence Borda (University of Sussex, UK)
Douglas Coates (Universidade Federal do Rio de Janeiro, Brasil)
Gabriela Estevez (Federal Fluminense University, Brasil)
Iacopo Longo (University of Exeter, UK)
Tanja Schindler (University of Exeter, UK and Jagiellonian University in Krakow, Poland)
Damien Thomien (Université Paris-Saclay, France)

The event is partly funded by the London Mathematical Society to celebrate Tanja Schindler's new appointment and partly funded by a seed funding grant to enhance collaboration between University of Exeter and Université Paris-Saclay. Moreover, Douglas Coates' visit is funded by the Heilbronn Institute for Mathematical Research. 

Schedule: 

Wednesday:    Introductory talks     11:00am  - 12:30pm     Newman Purple

Conference                      1:30pm  -    5:15pm     Newman Green

Iacopo Longo                1:30pm  -    2:30pm
Douglas Coates           3:00pm  -    4:00pm
        Damien Thomien        4:15pm  -    5:15pm 

    Reception   after 5:15pm

Thursday: Conference                       8:45am  -   12:30pm   Harrison 107

Gabriela Estevez         8:45am  -      9:45am
Bence Borda     10:15am  -   11:15am
Tanja Schindler          11:30am  -   12:30pm

Lecture rooms: Note that we are in different rooms for different parts of the conference. A campus map can be found here.

Lunch: We will not organize a formal joint lunch.  However, a number of us will head to  La Touche on Wednesday. Other on-campus lunch options are the following: Forum Kitchen, Innovation Center Cafe .  All of them are only a couple of steps away from the math department / lecture rooms.

Dinner: On Wednesday we plan to have a dinner at a restaurant closer to the city center / train station. If you plan to attend, we would appreciate it if you would complete the form linked above. 

Travel: The meeting will happen at the main University of Exeter (Streatham) campus which is approximately a 20 minute walk from Exeter St Davids train station, the main train station in Exeter. For those who don't want to walk up the steep hill to the campus, bus No 4 runs from the station to the University around every 15 minutes during peak times and there is also a taxi rank just outside the station.

Financial Support: At the moment we are not able to offer any financial support.

Any queries regarding other practical details should be sent to Tanja Schindler: t (dot) schindler (at) exeter (dot) ac (dot) uk . 

Organizer: Tanja Schindler

Titles and abstracts:

Bence Borda: Random behavior of circle rotations
One of the most classical examples of a dynamical system is the rotation of the circle group R/Z by a fixed irrational angle, and its higher dimensional analogue on the d-dimensional torus. Even though these systems are not chaotic, certain Birkhoff sums exhibit remarkable random behavior. We survey some old and recent results in the area, and discuss various approaches. In particular, we describe how spectral properties of the Gauss map and its generalizations related to continued fraction expansions lead to probabilistic limit theorems.

Douglas Coates: Evolution of measures for systems with parabolic fixed points
Maps with several equally and sufficiently sticky neutral fixed points can present *non-statistical behaviour* in the sense that the sequence of empirical measures does not converge for Lebesgue almost every inital condition. Such systems do not admit SRB measures or physical measures. We will show that nevertheless one can sometimes give a precise description of the long-term behaviour of the empirical measures in these situations. For example, one can determine the almost sure limit points of the empirical measures and prove that the empirical measures do in fact converge in distribution. Moreover, one can show the existence of a strong natural measure: a distinguished measure ν so that the push forwards of any absolutely continuous measure converge to ν. We will also discuss how there are some invariant measures whoose basin of attractions are of full Hausdorff dimension, despite being of zero Lebesgue measure. These are joints works with Ian Melbourne and Amin Talebi, and with Katrin Gelfert.

Gabriela Estevez: Some recent results for multicritical circle maps
Circle homeomorphisms without periodic points and with critical points belong to the boundary of chaos, i.e. the boundary between maps with zero and positive topological entropy. This class of maps has been studied since the 1980s but there are still lots of open problems. In this talk I will discuss some recent results related to the smoothness of the conjugacy between critical circle maps and I will explain the differences in the uncritical, bicritical and multicritical cases.

Iacopo Longo: Nonautonomous Differential Equations in the Presence of Bounded Noise
Nonautonomous systems subject to noise arise naturally in many applied contexts. Particularly relevant are those featuring time-dependent parameters and uncertainties, which may drive the emergence of tipping points. In this talk, we focus on the case of bounded noise, where the dynamics can be captured topologically via deterministic set-valued dynamical systems: initial conditions are evolved under all admissible noise realisations, abstracting from probabilistic details. However, as these systems operate on the space of nonempty compact subsets—a space lacking Banach structure—they pose substantial analytical and numerical challenges. In particular, bifurcation analysis of attractors remains a significant obstacle. To address this, we derive a higher-dimensional single-valued determinisitic dynamical system which characterizes the evolution of the boundary of invariant sets of certain differential inclusions.

Tanja Schindler: Trimmed laws of large numbers for different dynamical systems
Trimming, i.e. removing the largest summands of a sum of identically distributed (iid) random variables, has a long tradition to prove limit theorems which are not valid if one considers the untrimmed sum - one example is the strong law of large numbers for random variables with an infinite mean or in case of ergodic transformations Birkhoff's ergodic theorem. In this talk I will compare different dynamical systems, e.g. piecewise expanding interval maps and irrational rotations with the results for iid random variables regarding weak and strong laws of large numbers after trimming. This will be a somewhat expository talk.

Damien Thomien: Extension of dynamical systems and metastable states
A classical question about random walks is whether an excursion from 0 will hit a given level set or not. This can be answered using potential theory, as has been know since works by Kesten and Spitzer in the 1960s.
The framework of random walks can be significantly extended by considering instead extensions of dynamical systems, such as Lorentz gases. The study of excursions in this setting becomes much more delicate. In particular, it involves systems with metastable states, that is, systems with components between which transitions are rare. I'll present how these systems appear, and the consequences of the existence of these metastable states on the solutions of a Poisson equation and on the properties of excursions.