This is a virtual international seminar organized by Ilia Binder, Jacopo De Simoi, Zhiqiang Li, Federico Rodriguez-Hertz, and Mariusz Urbański. This seminar focuses on ergodic theory. We invite anyone interested to participate, and to volunteer talks.
The seminar runs on the second Tuesday of each month. We will have two speakers each time.
All seminars are held in the Zoom room with meeting ID 832 0847 3832 (Passcode: Ergodic).
Speaker 1: Dima Dolgopyat (University of Maryland, US)
Abstract: TBA
Speaker 2:
Abstract:
Speaker 1: Michael Yampolsky (University of Toronto, Canada)
Abstract: I will talk about the theoretical challenges to the numerical study of dynamical systems. I will broadly discuss what practitioners attempt to compute, and whether such computations are always possible. Such questions lead to interesting mathematics with surprising practical implications. As an instructive example of the limitations on our ability to compute things, I will describe a “nice” one-dimensional dynamical system for which a numerical approximation of the long-term statistical behavior of the orbits is not possible. In particular, the Monte Carlo simulation provably fails for it.
Speaker 2: Dima Dukdo (Stony Brook University, US)
Abstract: For surface self-homeomorphisms (e.g., pseudo-Anosov maps), the induced dynamics on isotopy classes of curves forms a well-established and fruitful theory. We will discuss analogous questions for postcritically finite (PCF) rational maps, such as the existence of spanning graphs of minimal entropy and the finite global attractor conjecture for the multivalued pullback operation on isotopy classes of graphs of prescribed complexity. We then prove the finiteness of such an attractor for maps with four postcritical points, excluding the usual Lattès counterexamples. The proof, which is joint work with L. Bartholdi and K. Pilgrim, relies on a detailed analysis of the non-uniform hyperbolicity of PCF correspondences on Riemann surfaces.
Speaker 1: Mark Pollicott (University of Warwick, UK)
Abstract: Livsic's famous theorem for hyperbolic systems states that a Holder continuous function which sums/integrates to zero around all closed orbits is necessarily a coboundary. Recently F. Rodriguez-Hertz and A. Gogolev proved an interesting Abelian Livsic Theorem whereby they assume the hypothesis on fewer closed orbits and still obtain a (slightly modified) conclusion. In this talk I will present a slightly different viewpoint, some related results and generalizations, and discuss various associated questions. This is joint work with Richard Sharp.
Speaker 2: Oliver Jenkinson (Queen Mary University of London, UK)
Abstract: Ergodic optimization investigates the properties of invariant measures that maximize (or minimize) the space average of a continuous potential function. Typical Periodic Optimization (TPO) is the phenomenon where, in spaces of regular functions, a generic function has a unique maximizing measure, and this measure is supported on a periodic orbit. Following Contreras' resolution of the TPO Conjecture for expanding open mappings, this talk will focus on extensions of this result to: - Symbolic systems, including all sofic shifts, by identifying the Markov boundary as the only possible source of failure of TPO (joint work with Wen Huang, Leiye Xu & Yiwei Zhang). - The problem of Joint TPO, where both the dynamical system and the potential are varied in suitable spaces, and the maximizing measure may again be generically periodic (joint work with Zelai Hao, Yinying Huang & Zhiqiang Li).
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We are looking for volunteer speakers. Contact one of the organizers to be added to the schedule.
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