One-Day Ergodic Theory Meeting University of Exeter, 15 June 2022
Schedule
We will host a One Day Ergodic Theory Meeting at the University of Exeter on Wednesday 15th June 2022. All the talks will be held in Room 203 of the Harrison Building. The schedule for the day is as follows:
12:30 - 14:00 Informal lunch at La Touche for those arriving early enough (meet at the entrance to Harrison Building at 12.15)
14:00 - 15:00 Surabhi Desai (University of Exeter)
15:00 - 15:10 Break
15:10 - 16:10 Jamie Walton (University of Nottingham)
16:10 - 16:40 Coffee break
16:40 - 17:40 Jonathan Fraser (University of St Andrews)
18:00 Leave for drinks/dinner (meet at the entrance to Harrison Building)
If you would like to join for dinner (we plan to go to Mill on the Exe), please let me know (ideally by 12pm on Monday 13th June 2022).
If you have any questions, please do not hesitate to get in touch with either myself (d.d.allen "at" exeter "dot" ac "dot" uk) or Mark Holland (m.p.holland "at" exeter "dot" ac "dot" uk).
This meeting is part of the network of One-Day Ergodic Theory meetings between Birmingham University, Bristol University, Exeter University, Loughborough University, Manchester University, Queen Mary, St. Andrews University, and Warwick University funded by a scheme 3 LMS grant.
Titles and Abstracts
Surabhi Desai (University of Exeter)
Dynamical Borel-Cantelli lemmas on general target sets
Abstract: In probability theory, the Borel-Cantelli lemma can be used to determine the probability that infinitely many events occur in some sequence of events. In a dynamical setting, we may establish analogous properties on sequences of shrinking target sets. Typically, such target sets shrink to a point. In this talk, we shall focus on dynamical Borel-Cantelli properties in the context of sequences of sets which shrink to more general classes of sets.
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Jamie Walton (University of Nottingham)
Substitutions over infinite alphabets and unique ergodicity
Abstract: A substitution rule is a procedure for replacing tiles with larger patches of tiles (geometric or symbolic in one dimension) that can be iterated to define tilings of Euclidean space with aperiodic order. Famous examples include the Penrose tilings and, from symbolic dynamics, the Fibonacci, Thue-Morse and period doubling sequences. The theory is well understood when the set of prototiles or ‘alphabet’, in the symbolic case, is finite. In this talk I will present joint work with Neil Mañibo and Dan Rust which considers an extension of the theory to infinite alphabets. To retain some of the flavour of the finite setting, we choose to work with continuous substitutions on alphabets equipped with a compact Hausdorff topology. We find sufficient conditions on the substitution for the resulting tiling dynamical system to be uniquely ergodic. Many results rely on the theory of positive operators on Banach spaces, where the traditional substitution matrix is replaced with the substitution operator on continuous functions over the alphabet.
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