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
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 May 10

# Dynamics & probability: Tamar Ziegler (HUJI) - Concatenating characteristic factors

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
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)
2016 Jun 07

# Dynamics & probability: Hillel Furstenberg (HUJI): Algebraic numbers and homogeneous flows

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)
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 Mar 08

# Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part I)

12:00pm to 1:45pm

## Location:

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.
2016 Jun 07

# Dynamics lunch:Asaf Katz - Uniqueness of measure of maximal entropy

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Jan 05

# Dynamics lunch: Sebastian Donoso (HUJI) - Automorphism groups of low complexity subshifts

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
Abstract: The automorphism group of a subshift $(X,\sigma)$ is the group of homeomorphisms of $X$ that commute with $\sigma$. It is known that such groups can be extremely large for positive entropy subshifts (like full shifts or mixing SFT). In this talk I will present some recent progress in the understanding of the opposite case, the low complexity one. I will show that automorphism groups are highly constrained for low complexity subshifts. For instance, for a minimal subshifts with sublinear complexity the automorphism group is generated by the shift and a finite set.
2016 May 31

# Dynamics lunch: Yuri Kifer (HUJI) - On Erdos-Renyi law of large numbers and its extensions

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 May 10

# Dynamics lunch: Ori Gurel Gurevitch (HUJI), Stationary random graphs

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Mar 22

# Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part III)

12:00pm to 1:45pm

Ross 70
2015 Dec 29

# Dynamics lunch: Tom Gilat (HUJI): "Measure rigidity for `dense' multiplicative semigroups (following Einsiedler and Fish)"

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Jun 21

# Dynamics lunch: Genadi Levin - Monotonicity of entropy in real quadratic family'

12:00pm to 1:00pm

## Location:

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