When: Thursday, 26 June 2025
Where: University of Exeter, Streatham Campus, Newman Purple Lecture hall within the Peter Chalk Centre.
The One Day Ergodic Theory Meeting is a "wandering" seminar series supported by an LMS grant and organised by 10 UK universities: Birmingham, Bristol, Durham, Exeter, Loughborough, Manchester, The Open University, Queen Mary, St. Andrews and Warwick.
In June 2025 the One Day Ergodic Theory Meeting will be hosted by the University of Exeter as a satellite event of the joint British Mathematical Colloquium and British Applied Mathematics Colloquium (BMC-BAMC). To attend this One Day Ergodic Theory Meeting, there is no registration nor any fee, and one does not have to be a participant of the BMC-BAMC. However, to help us minimise 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.
Titles and abstracts:
Rational points near manifolds and Khintchine theorem (Shreyasi Datta)
In this talk, I will try to explain some old and new ideas combining homogeneous dynamics and counting rational points near a manifold. We show how this is applied to prove a Khintchine type result for any nondegenerate manifold. Joint work with Victor Beresnevich.
The talk is based on https://arxiv.org/abs/2505.01227.
Statistical Chaos for systems away from equilibrium (Zemer Kosloff)
A common definition of chaos (disorder) for measure preserving diffeomorphisms is that the system can simulate a random system (eg. Bernoulli shift). We will discuss the limitations of this definition for (Baire) generic diffeomorphisms with respect to the volume measure and a suggestion of a better notion involving finitary (almost everywhere continuous) stationary factors. This will be demonstrated via the model of Anosov (hyperbolic) diffeomorphisms.
This is a joint work with Terry Soo (UCL).
Wandering domains and non-autonomous dynamics (Gwyneth Stallard)
Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, there is a fascinating array of possible types of wandering domains. New results on the relationship between the behaviour of orbits of points in the interior of wandering domains, and orbits of points on the boundary can be proved in a very general context. We show how this has led to a generalisation of results from ergodic theory concerning recurrence and shrinking targets to the setting of boundary dynamics for non-autonomous systems of holomorphic maps.
Lunch: As we assume that a lot of people get lunch from the BMC-BAMC, we will not organize a joint lunch. For those coming to the One Day Ergodic Theory Meeting separate to the BMC-BAMC, we suggest the following on-campus lunch options: Forum Kitchen, Innovation Center Cafe, La Touche. All of them are only a couple of steps away from the math department.
Dinner: We plan to have a network 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.
For full details on previous editions of the One Day Ergodic Theory Meeting, please visit the Central One Day Ergodic Theory webpage.
Financial Support: Some support is available for participants, and any queries regarding support should be sent to Thomas Jordan: thomas (dot) jordan (at) bristol (dot) ac (dot) uk .
Any queries regarding other practical details should be sent to Tanja Schindler: t (dot) schindler (at) exeter (dot) ac (dot) uk .
Local organizers: Mark Holland, Tony Samuel, Tanja Schindler