Talks
Long Talks:
Dominik Kwietniak, Title: An anti-classification theorem for the topological conjugacy problem for Cantor minimal systems
Abstract: The isomorphism problem in dynamics dates back to a question of von Neumann from 1932: Is it possible to classify the ergodic measure-preserving diffeomorphisms of a compact manifold up to isomorphism? Foreman, Rudolph and Weiss [Ann. of Math. (2) 173 (2011), no. 3, 1529-1586.] proved an anti-classification theorem that rigorously explains why, in a certain sense, such a classification is impossible. We study a topological analogue of von Neumann's problem. Let Min(C) stand for the Polish space of all minimal homeomorphisms of the Cantor set C. Recall that a homeomorphism T of C is minimal if every orbit of T is dense in C. We say that S and T in Min(C) are topologically conjugate if there is a homeomorphism h of C such that Sh=hT. We will discuss an anti-classification result, saying that it is impossible to tell if two minimal Cantor set homeomorphisms are topologically conjugate using only a countable amount of information and computation. We will explain, how to understand such an anti-classification result and why it suffices to show that the topological conjugacy relation of Cantor minimal systems treated as a subset of Min(C) x Min(C) is complete analytic, so a non-Borel subset of Min(C) x Min(C). This is joint work with Konrad Deka, Felipe García-Ramos, Kosma Kasprzak, Philipp Kunde (all from the Jagiellonian University in Kraków).
Tanja Schindler, Title: Limit Theorems for a class of unbounded observables with an application to "Sampling the Lindelöf hypothesis"
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 quantitativecentral 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.
Maciej Wojtkowski, Title: Arithmetic properties of some rotations and interval maps via linear "recurrencies"
Abstract: Download the abstract in PDF