Title: Approximations of groups and equations over groups.
Abstract:
The talk is largely based on the paper which may be found here: https://authors.elsevier.com/a/1UN3b4~FOr6ze
Title: Old and New Results on Subgroup Growth in Pro-p Groups.
Abstract: I will survey our current knowledge about subgroup growth in pro-p growth. In particular I will present new solutions to long standing open problems in the area:
1. What is the minimal subgroup growth of non-$p$-adic analytic pro-$p$ groups? (Joint work with Benjamin Klopsch and Jan-Christoph Schlage-Puchta.)
2. What are the subgroup growths of the Grigorchuk group and the Gupta-Sidki groups? (Joint work with Jan-Christoph Schlage-Puchta.)
Title: Inp-minimal ordered groups.
Abstract. The main goal of the talk is to present the proof of the theorem stating that inp-minimal (left)-ordered groups are abelian. This generalizes a previous result of P. Simon for bi-ordered inp-minimal groups.
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
some averages.
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.
Consider a sequence of random walks on $\mathbb{Z}/p\mathbb{Z}$ with symmetric generating sets $A= A(p)$. I will describe known and new results regarding the mixing time and cut-off. For instance, if the sequence $|A(p)|$ is bounded then the cut-off phenomenon does not occur, and more precisely I give a lower bound on the size of the cut-off window in terms of $|A(p)|$. A natural conjecture from random walk on a graph is that the total variation mixing time is bounded by maximum degree times diameter squared.
Title: Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation.
Abstract:
We consider an analytic curve $\varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R})$ and embed it into some homogeneous space $G/\Gamma$, and translate it via some diagonal flow
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
classification in particular yields the negative answer to Gowers'
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.
