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
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.

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

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.

2016
Jun
07

12:00pm to 1:00pm

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

2016
Jan
05

12:00pm to 1:00pm

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

12:00pm to 1:00pm

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

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

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

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
Jan
20

11:00am to 12:45pm

Ross building, Hebrew University (Seminar Room 70A)

Abstract: One of the first applications of model categories was Quillen homology. Building on the notion of Beck modules, one defines the cotangent complex of an associative or commutative (dg)-algebras as the derived functor of its abelianization. The latter is a module over the original algebra, and its homology groups are called the (Andre'-)Quillen homology. The caveat of this approach is that the cotangent complex is not defined as a functor on the category of all algebras.

2015
Nov
11

11:00am to 12:45pm

Ross building, Hebrew University (Seminar Room 70A)

Abstract: An elastic energy functional of a Riemannian manifold is a function that measures the distance of an embedding u:→ℝd from being isometric. In many applications, the manifold in consideration is actually a limit of other manifolds, that is, is a limit of n in some sense. Assuming that we have an elastic energy functional for each n, can we obtain an energy functional of which is a limit of the functionals of n?