Dynamical & Probability

The Dynamics & Probability Seminar meets every Tuesday at 14:15 at Ross 70.
The HUJI dynamics group webpage can be found here.

2018 Jun 26

Sieye Ryu (BGU): Predictability and Entropy for Actions of Amenable Groups and Non-amenable Groups

2:15pm to 3:15pm

Suppose that a countable group $G$ acts on a compact metric space $X$ and that $S \subset G$ is a semigroup not containing the identity of $G$. If every continuous function $f$ on $X$ is contained in the closed algebra generated by $\{sf : s \in S\}$, the action is said to be $S$-predictable. In this talk, we consider the following question due to Hochman: When $G$ is amenable, does $S$-predictability imply zero topological entropy? To provide an affirmative answer, we introduce the notion of a random invariant order.
2018 May 22

Barak Weiss (TAU): New examples for the horocycle flow on the moduli space of translation surfaces

2:15pm to 3:15pm

A longstanding open question concerning the horocycle flow on moduli space of translation surfaces, is whether one can classify the invariant measures and orbit-closures for this action. Related far-reaching results of Eskin, Mirzakhani and Mohammadi indicated that the answer might be positive. However, in recent work with Jon Chaika and John Smillie, we find unexpected examples of orbit-closures; e.g. orbit closures which are not generic for any measure, and others which have fractional Hausdorff dimension. Such examples exist even in genus 2.
2018 Jun 19

Tomasz Rzepecki (Uniwersytet Wrocławski): Topological dynamics and Galois groups in model theory

2:15pm to 3:15pm

Location: 

Ross 70
In recent years, topological dynamics have become an important tool in model theory. I will talk about some topological dynamical results from my PhD thesis about the so-called group-like equivalence relations. I plan to give a glimpse of the motivations in model theory (mostly related to the model-theoretic Galois groups and connected components of definable groups) and to show some ideas of the proofs. I will briefly recall the required notions from topological dynamics. Some knowledge of model theory will help to understand the motivations, but otherwise, it will not be necessary.
2018 May 08

Dynamics Seminar: Tsviqa Lakrec (Huji)

12:00pm to 1:00pm

Location: 

Manchester 209
Consider a simple random walk on $\mathbb{Z}$ with a random coloring of $\mathbb{Z}$. Look at the sequence of the first $N$ steps taken and colors of the visited locations. From it, you can deduce the coloring of approximately $\sqrt{N}$ integers. Suppose an adversary may change $\delta N$ entries in that sequence. What can be deduced now? We show that for any $\theta<0.5,p>0$, there are $N_{0},\delta_{0}$ such that if $N>N_{0}$ and $\delta<\delta_{0}$ then with probability $>1-p$ we can reconstruct the coloring of $>N^{\theta}$ integers.
2018 May 29

Yuri Lima (Paris 11): Symbolic dynamics for non-uniformly hyperbolic systems with singularities

2:15pm to 3:15pm

Location: 

Ross 70
Symbolic dynamics is a tool that simplifies the study of dynamical systems in various aspects. It is known for almost fifty years that uniformly hyperbolic systems have ``good'' codings. For non-uniformly hyperbolic systems, Sarig constructed in 2013 ``good'' codings for surface diffeomorphisms. In this talk we will discuss some recent developments on Sarig's theory, when the map has discountinuities and/or critical points, such as multimodal maps of the interval and Bunimovich billiards.
2018 May 08

Dynamics Seminar: Yinon Spinka (TAU): Finitary codings of Markov random fields

2:15pm to 4:15pm

Location: 

Ross 70
Let X be a stationary Z^d-process. We say that X is a factor of an i.i.d. process if there is a (deterministic and translation-invariant) way to construct a realization of X from i.i.d. variables associated to the sites of Z^d. That is, if there is an i.i.d. process Y and a measurable map F from the underlying space of Y to that of X, which commutes with translations of Z^d and satisfies that F(Y)=X in distribution. Such a factor is called finitary if, in order to determine the value of X at a given site, one only needs to look at a finite (but random) region of Y.
2018 Jun 05

Tom Meyerovitch (BGU): On expansivness, topological dimension and mean dimesnion

2:15pm to 3:15pm

Location: 

Ross 70
Expansivness is a fundamental property of dynamical systems. It is sometimes viewed as an indication to chaos. However, expansiveness also sets limitations on the complexity of a system. Ma\~{n}'{e} proved in the 1970’s that a compact metric space that admits an expansive homeomorphism is finite dimensional. In this talk we will discuss a recent extension of Ma\~{n}'{e}’s theorem for actions generated by multiple homeomorphisms, based on joint work with Masaki Tsukamoto. This extension relies on a notion called “topological mean dimension’’ , introduced by Gromov and

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