# 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
2018 Apr 24

2:00pm to 3:00pm

2018 Apr 10

2:15pm to 3:15pm

2018 May 01

2:00pm to 3:00pm

2018 Apr 17

2:15pm to 3:15pm

Ross 70
2018 Mar 27

2:15pm to 3:15pm

2018 Jan 30

# Action Now Seminar: Menny Aka (ETH), "On rational planes in four-dimensional space and their associated lattices"

4:00pm to 5:00pm

## Location:

IIAS, HUJI, Feldman Building, Room 130
2018 Jan 30

# Action Now Seminar: Tammy Ziegler (HUJI), "Dynamics, arithmetic progressions and approximate cohomology"

10:00am to 11:00am

## Location:

IIAS, HUJI, Feldman Building, Room 130