2016
Mar
08

# Dynamics & probability: Elon Lindenstrauss (Mean dimension and embedding of Z^d actions)

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Mar
08

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Mar
29

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Abstract:
There are by now several celebrated measure classification results to the effect that a measure is uniform provided it possesses sufficient "invariance" as quantified by stabilizer, entropy, or recurrence. In some applications, part of the challenge is to identify or construct measures to which these hypotheses apply.

2016
May
10

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Mar
15

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Jun
07

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

2016
Jan
12

1:45pm to 2:45pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

In the paper "Mean dimension, small entropy factors and an
embedding theorem, Inst. Hautes Études Sci. Publ. Math 89 (1999)
227-262", Lindenstrauss showed that minimal systems of mean dimension
less than $cN$ for $c=1/36$ embed equivariantly into the Hilbert cubical
shift $([0,1]^N)^{\mathbb{Z}}$, and asked what is the optimal value
for $c$. We solve this problem by proving that $c=1/2$. The method of
proof is surprising and uses signal analysis sampling theory. Joint
work with Masaki Tsukamoto.

2016
Jun
21

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Let $A$, $B$ be two rational functions of degree at least two on the Riemann sphere.
The function $B$ is said to be semiconjugate to the function $A$ if there exists a non-constant rational function $X$ such that the equality (*) A\circ X=X\circ B holds.
The semiconjugacy relation plays an important role in the classical theory of complex dynamical systems as well as in the new emerging field of arithmetic dynamics. In the talk we present a description of solutions of (*) in terms of two-dimensional orbifolds of non-negative Euler characteristic on the Riemann sphere.

2016
May
31

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

20 years ago Benjy Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions. In this talk we will present a construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such a measure. We will also discuss "uniformly recurrent" entire functions, their connection to such constructions, and their possible growth. The talk is based on a joint work with Lev Buhovski, Alexander Loganov, and Mikhail Sodin.

2016
Apr
05

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

We give a brief overview on applications of the Poincare's equation to the study of random walk on the the Sierpi ́nski gasket. In particular, we discuss such questions as anomalous diffusion, relation to branching processes and decimation invariance. Metods of the complex analysis and the iteration theory are used to deal with the aforemen-tioned problems.

2016
Jan
05

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Abstract:
We will present an elementary problem and a conjecture regarding percolation on planar graphs suggested by assuming quasi invariance of percolation crossing probabilities under coarse conformal uniformization.

2016
Jun
14

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Let S be a finite set (the sample space), and
f_i: S -> R functions, for 1 ≤ i ≤ k. Given a k-tuple (v_1,...,v_k) in R^k
it is natural to ask:
What is the distribution P on S that maximizes the entropy
-Σ P(x) log(P(x))
subject to the constraint that the expectation of f_i be v_i?
In this talk I'll discuss a closed formula for the solution P
in terms of a sum over cumulant trees. This is based on a general calculus
for solving perturbative optimization problems due to Feynman, which may be
of interest in its own right.

2016
May
17

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Abstract: This talk will introduce the notion of Gaussian and almost Gaussian log-correlated fields. These are a class of random (or almost random) functions many of whose statistics are predicted to coincide in a large system-size limit. Examples of these objects include:
(1) the logarithm of the Riemann zeta function on the critical line (conjecturally)
(2) the log-characteristic polynomial of Haar distributed unitary random matrices (and others),
(3) the deviations of Birkhoff sums of substitution dynamical systems (conjecturally)

2015
Nov
10

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Self-affine measures with equal Hausdorff and Lyapunov dimensions
Abstract:
Let μ be the stationary measure on ℝd which corresponds to a self-affine iterated function system Φ and a probability vector p. Denote by A⊂Gl(d,ℝ) the linear parts of Φ. Assuming the members of A contract by more than 12, it follows from a result by Jordan, Pollicott and Simon, that if the translations of Φ are drawn according to the Lebesgue measure, then dimHμ=min{D,d} almost surely. Here D is the Lyapunov dimension, which is an explicit constant defined in terms of A and p.

2015
Dec
15

2:00pm to 4:30pm

Manchester building, Hebrew University of Jerusalem, 209

Abstract:

2015
Nov
17

2:00pm to 3:00pm

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Topological structures and the pointwise convergence of some averages for commuting transformations
Abstract: ``Topological structures'' associated to a topological dynamical
system are recently developed tools in topological dynamics. They have
several applications, including the characterization of topological
dynamical systems, computing automorphisms groups and even the pointwise
convergence of some averages. In this talk I will discuss some developments
of this subject, emphasizing applications to the pointwise convergence of
some averages.