Eventss

2016 Jun 14

Dynamics & probability: Amitai Zernik (HUJI): A Diagrammatic Recipe for Computing Maxent Distributions

2:00pm to 3:00pm

Location: 

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

Dynamics & probability: Elliot Paquette (Weizmann) - Almost gaussian log-correlated fields

2:00pm to 3:00pm

Location: 

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)
2016 Jan 12

Dynamics & prob. [NOTE SPECIAL TIME!!], Yonatan Gutman (IMPAN) - Optimal embedding of minimal systems into shifts on Hilbert cubes

1:45pm to 2:45pm

Location: 

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

Dynamics & probability: Fedor Pakovitch - On semiconjugate rational functions

2:00pm to 3:00pm

Location: 

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.
2016 May 31

Dynamics & probability: Adi Glücksam (TAU): Translation invariant probability measures on the space of entire functions

2:00pm to 3:00pm

Location: 

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

Dynamics & probability: Grisha Derfel (BGU): “Diffusion on fractals and the Poincare's functional equation"

2:00pm to 3:00pm

Location: 

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 12

Dynamics lunch: Brandon Seward (HUJI), "Borel chromatic numbers of free groups"

12:00pm to 1:00pm

Location: 

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

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