2016
Mar
15

# Dynamics & probability: Mike Hochman "Dimension of Furstenberg measure for SL_2(R) random matrix products"

2:00pm to 3:00pm

## Location:

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

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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
Nov
03

10:30am to 11:30am

Ross 70

Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.

2016
May
10

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

2016
Mar
22

2015
Dec
29

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

2016
Jun
21

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

2016
Jan
12

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

Borel chromatic numbers of free groups
Abstract:
Recall that a coloring of a graph is a labeling of its vertices such that
no pair of vertices joined by an edge have the same label. The chromatic
number of a graph is the smallest number of colors for which there is a
coloring.
If G is a finitely generated group with generating set S, then for any free
action of G on a standard Borel space X, we can place a copy of the
S-Cayley graph of G onto every orbit. This results in a graph whose vertex
set is X and whose edge set is Borel measurable. We can then consider Borel

2016
May
17

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

I will describe Bilu's equidistribution theorem for roots of polynomials, and explain some implications this has on entropy of toral automorphisms.

2016
Apr
05

12:00pm to 1:00pm

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)

2016
Mar
08

12:00pm to 1:45pm

Ross 70

Entropy was first defined for actions of the integers by Kolmogorov in 1958 and then extended to actions of countable amenable groups by Kieffer in 1975. Recently, there has been a surge of research in entropy theory following groundbreaking work of Lewis Bowen in 2008 which defined entropy for actions of sofic groups. In this mini-course I will cover these recent developments. I will carefully define the notions of sofic entropy (for actions of sofic groups) and Rokhlin entropy (for actions of general countable groups), discuss many of the main results, and go through some of the proofs.