# Dynamical & Probability

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

2019 Mar 26

# Dynamics Seminar: Nattalie Tamam "Diagonalizable groups with non-obvious divergent trajectories"

12:00pm to 1:00pm

## Location:

Manchester faculty club
Singular vectors are the ones for which Dirichlet’s theorem can be infinitely improved. For example, any rational vector is singular. The sequence of approximations for any rational vector q is 'obvious'; the tail of this sequence contains only q. In dimension one, the rational numbers are the only singulars. However, in higher dimensions there are additional singular vectors. By Dani's correspondence, the singular vectors are related to divergent trajectories in Homogeneous dynamical systems. A corresponding 'obvious' divergent trajectories can also be defined.
2019 Mar 07

1:30pm to 2:30pm

Ross 70
2019 Mar 07

# Alexandre Danilenko (ILTPE) Forcing conservativeness of nonsingular Bernoulli shifts.

4:15pm to 5:15pm

Abstract: We first survey a recent progress related to the nonsingular Bernoulli transformations. Then we construct inductively new examples of conservative Bernoulli maps of type III. They appear as a limit of a sequence of Bernoulli maps of type II_1.
2019 Mar 07

# Emmanuel Roy (Paris 13) Non-singular Poisson suspensions

2:45pm to 3:45pm

## Location:

Ross 70
Poisson suspensions are random sets of points endowed with a transformation that displaces each point according to a single transformation of the sigma-finite space where the points lie. In this ongoing work, instead of dealing with measure-preserving transformations (which is the classical case), we are going to present our attempt to explore the non-singular case. The difficulties are counterbalanced by new tools that are trivial in the measure-preserving case but highly informative in the non-singular one. We will present these tools as well as the first basic results we’ve obtained.
2019 Mar 26

2:15pm to 3:15pm

Abstract:
2019 Apr 30

2:15pm to 3:15pm

2019 May 14

2:15pm to 3:15pm

2019 Mar 12

# Dynamics Seminar: Terry Soo (KU) Finitary isomorphism of Bernoulli flows

2:15pm to 3:15pm

## Location:

Ross 70
A powerful theory due to Ornstein and his collaborators has been successfully applied to many random systems to show that they are isomorphic to independent and identically distributed systems. The isomorphisms provided by Ornstein's theory may not be finitary, that is, effectively realizable in practice. Despite the large number of systems known to be Bernoulli, there are only a handful of cases where explicit finitary isomorphisms have been constructed. In this talk, we will discuss classical and recent constructions, and some long standing open problems.
2019 Mar 19

# Dynamics Seminar: Elon Lindenstrauss (HUJI) - Double variational principle for mean dimension

2:15pm to 3:15pm

Mean dimension is a topological invariant of dynamical systems introduced by Gromov that measures the number of parameters per iteration needed to describe a trajectory in the system. We characterize this invariant (at least for dynamical systems with the marker property, such as infinite minimal systems) using a min-max principle, where choices of both a metric on the topological space and an invariant probability measure on the system are varied. The work I will report on is joint work with M. Tsukamoto.
2019 Apr 02

2:15pm to 3:15pm

2019 Jan 01

# Yotam Smilansky (HUJI), Multiscale substitution schemes and Kakutani sequences of partitions.

2:15pm to 3:15pm

## Location:

Ross 70
Abstract: Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. In this talk we will use new path counting results for directed weighted graphs to show that such sequences of partitions are uniformly distributed, thus extending Kakutani's original result. Furthermore, we will describe certain limiting frequencies
2018 Dec 25

# Ofer Shwartz (Weizmann) Convergence along the cutting-sequences of the geodesic flow

2:15pm to 3:15pm

## Location:

Ross 70
The geodesic flow on a normal cover of a compact hyperbolic surface admits a "random walk" on the group of decks transformations $G$. In this talk, I'll provide some recent results which connect this walk to the geometric properties of the cover and $G$.
2018 Nov 27

# Yan Dolinsky. A new type of stochastic target problems.

12:00pm to 1:00pm

## Location:

Coffee lounge
Abstract: I will discuss two stochastic target problem in the Brownian framework . The first problem has a nice solution which I will present. The second problem is much more complicated and for now remains open. I will discuss the challenges and connection with other fields in probability theory.
2019 Jan 08

# Godofredo Iommi (PUC), Upper semi-continuity of the entropy map for Markov shifts

2:15pm to 3:15pm

Abstract: In this talk I will show that for finite entropy countable Markov shifts the entropy map is upper semi-continuous when restricted to the set of ergodic measures. This is joint work with Mike Todd and Anibal Velozo.
2019 Jan 15

# Yeor Hafouta (HUJI) A local limit theorem for random dynamical systems.

2:15pm to 3:15pm

## Location:

Ross 70
Probabilistic limit theorems for (distance expanding and hyperbolic) dynamical systems is a well studied topic. In this talk I will present conditions guaranteeing that a local central limit theorem holds true for certain families of distance expanding random dynamical systems. If time permits, I will also discuss a version of the Berry-Esseen theorem. Joint work with Yuri Kifer.