Fractal Pattern

The Long Run—Topics in Ergodic Theory

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).

Dates for 2026:
Date & Time:
  • May 12, 10am-12pm US Eastern time/ May 12, 4-6pm CEST time/ May 12, 10pm-12am China time/ May 12, 3-5pm UK time

Speaker 1: Mark Pollicott (University of Warwick, UK)

Title: Livsic's theorem revisited

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)

Title: (Joint) Typical Periodic Optimization

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).

Date & Time:
  • Jun 9, 10am-12pm US Eastern time/ Jun 9, 4-6pm CEST time/ Jun 9, 10pm-12am China time

Speaker 1: Michael Yampolsky (University of Toronto, Canada)

Title: How to lose at Monte Carlo

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)

Title: TBC

Abstract: TBC

Logistics and Mailing List

If you would like to subscribe to the mailing list, please send an email with title Subscribe to: subscribethelongrun@hotmail.com.

We are looking for volunteer speakers. Contact one of the organizers to be added to the schedule.

Also, we may consider using the email list for announcements of more broad interest to our community. Contact one of the organizers if you wish to post such an announcement.