There will be an ergodic theory meeting at the University of Warwick on Wednesday 23 October 2024. This is part of an LMS Scheme 3 funded network involving the following universities: Birmingham, Bristol, Durham, Exeter, Glasgow, Loughborough, Manchester, Open, Queen Mary, St Andrews and Warwick. For information about other meetings in the series, see
https://people.maths.bris.ac.uk/~matmj/LMSergodicmeetings.html
If you are from a university in the network and would like to request financial support to attend, please contact Thomas Jordan at thomas.jordan@bristol.ac.uk
All talks will take place in room MS.02 of the Zeeman Building. (Click here for a downloadable campus map.) After entering the Zeeman Building, the room is in front of you on the right. A group of people will go for lunch at 12:30pm, meeting by the Zeeman Building main entrance. We will go to dinner after the talks.
Schedule:
2:00pm-3:00pm: Mike Hochman (HUJI)
Strongly irreducible subshifts without periodic points
3:00pm-3:30pm: Tea break
3:30pm-4:30pm: Tanja Schindler (Exeter)
A qualitative central limit theorem for certain unbounded observables over piecewise expanding interval maps
4:30pm-4:45pm: Short break
4:45pm-5:45pm: Meng Wu (Oulo)
On normal numbers in fractals
Abstracts:
Mike Hochman: Strongly irreducible subshifts without periodic points
Abstract: A symbolic system is strongly irreducible if there is some g>0 such that any two patterns in the subshift can be glued together as long as they are separated by a gap of size g. This is the strongest mixing condition one can place on a symbolic system, and it implies many good properties, especially in combination with the finite type property: For example, globally supported measures of maximal entropy, a Krieger-type embedding theorem, and more. In my talk I will discuss the question of the existence of periodic points in such systems, and its connection to a question about periodic points in higher-dimensional shifts of finite type.
Tanja Schindler: A qualitative central limit theorem for certain unbounded observables over piecewise expanding interval maps
Abstract: Many limit theorems in ergodic theory are proven using the spectral gap method. So one of the main ingredients for this method is to have a space on which the transfer operator has a spectral gap. However, most of the classical spaces, like for example the space of Hölder or quasi-Hölder function or BV functions, don't allow unbounded functions. We will give such a space which allows observables with a pole at the fixed points of a piecewise expanding interval transformation and state a quantitative central limit theorem using Edgeworth expansions. As an application we give a sampling result for the Riemann-zeta function over a Boolean type transformation. This is joint work with Kasun Fernando.
Meng Wu: On normal numbers in fractals
Abstract: Given any Bernoulli measure μ that is x3 invariant (such as the Cantor-Lebesgue measure on the ternary Cantor set) and an irrational number t, it holds that for almost all x with respect to μ, the product tx is x3 normal (meaning that the orbit of tx under the x3 map is uniformly distributed on [0,1]). This result was recently proved by Dayan, Ganguly, and Barak Weiss using techniques from random walk theory. We will present a new proof of the Dayan-Ganguly-Weiss result, relying on recent advancements in the study of self-similar measures with overlaps. Our approach extends the result to cases where the measure μ is only required to be invariant, ergodic, and of positive dimension.
