Abstract:
In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.
All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.
Ross building, Hebrew University of Jerusalem, (Room 70)
To every topological group, one can associate a unique universal
minimal flow (UMF): a flow that maps onto every minimal flow of the
group. For some groups (for example, the locally compact ones), this
flow is not metrizable and does not admit a concrete description.
However, for many "large" Polish groups, the UMF is metrizable, can be
computed, and carries interesting combinatorial information. The talk
will concentrate on some new results that give a characterization of
metrizable UMFs of Polish groups. It is based on two papers, one joint
Ross building, Hebrew University of Jerusalem, (Room 70)
To every topological group, one can associate a unique universal
minimal flow (UMF): a flow that maps onto every minimal flow of the
group. For some groups (for example, the locally compact ones), this
flow is not metrizable and does not admit a concrete description.
However, for many "large" Polish groups, the UMF is metrizable, can be
computed, and carries interesting combinatorial information. The talk
will concentrate on some new results that give a characterization of
metrizable UMFs of Polish groups. It is based on two papers, one joint
Speaker: Oren Becker
Title: Locally testable groups
Abstract:
Arzhantseva and Paunescu [AP2015] showed that if two permutations X and Y in Sym(n) nearly commute (i.e. XY is close to YX), then the pair (X,Y) is close to a pair of permutations that really commute.
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
Manchester building, Hebrew University of Jerusalem, (Room 209)
The Danzer problem and a solution to a related problem of Gowers
Is there a point set Y in R^d, and C>0, such that every convex
set of volume 1 contains at least one point of Y and at most C? This
discrete geometry problem was posed by Gowers in 2000, and it is a special
case of an open problem posed by Danzer in 1965. I will present two proofs
that answers Gowers' question with a NO. The first approach is dynamical;
we introduce a dynamical system and classify its minimal subsystems. This
Title: Local limit theorem for certain ballistic random walks in random
environments
Abstract: We study the model of random walks in random environments in
dimension four and higher under Sznitman's ballisticity condition (T').
We prove a version of a local Central Limit Theorem for the model and also
the existence of an equivalent measure which is invariant with respect
to the point of view of the particle. This is a joint work with Noam Berger
and Moran Cohen.
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.
Repeats every week every Monday until Sun Nov 08 2015 .
11:00am to 1:00pm
Abstract:
Expander graphs have many wonderful properties, and have been an immensely useful and fruitful area of research in both applicative and theoretical fields. There has been a lot of interest recently in the study of higher dimensional generalizations of expanders to d-uniform hypergraphs. Many competing definitions have been proposed, and different definitions may be appropriate depending on the property of expanders that we wish to preserve.
Repeats every week every Tuesday until Tue Jan 24 2017 except Tue Nov 01 2016.
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
Given a Z^d shift of finite type and a finite range shift-invariant interaction, we present sufficient conditions for efficient approximation of pressure and, in particular, topological entropy. Among these conditions, we introduce a combinatorial analog of the measure-theoretic property of Gibbs measures known as strong spatial mixing and we show that it implies many desirable properties in the context of symbolic dynamics. Next, we apply our
