Abstract: A circle packing is a canonical way of representing a planar graph. There is a deep connection between the geometry of the circle packing and the proababilistic property of recurrence/transience of the simple random walk on the underlying graph, as shown in the famous He-Schramm Theorem. The removal of one of the Theorem's assumptions - that of bounded degrees - can cause the theorem to fail. However, by using certain natural weights that arise from the circle packing for a weighted random walk, (at least) one of the directions of the He-Schramm Theorem remains true.

Abstract: Host proved a strengthening of Rudolph and Johnson's measure rigidity theorem: if a probability measure is invariant, ergodic and has positive entropy for the map x2 mod 1, then a.e. point equidisitrbutes under x3 mod 1. Host also proved a version for toral endomorphisms, but its hypotheses are in some ways too strong, e.g. it requires one of the maps to be expanding, so it does not apply to pairs of  automorphisms. In this talk I will present an extension of Host's result (almost) to its natural generality.

Abstract:
A restricted permutation of a locally finite directed graph $G=(V,E)$ is a vertex permutation $\pi: V\to V$ for which $(v,\pi(v))\in E$, for any vertex $v\in V$. The set of such permutations, denoted by $\Omega(G)$, with a group action induced from a subset of graph isomorphisms form a topological dynamical system. In the particular case presented by Schmidt and Strasser (2016), where $V=\mathbb{Z}^d$ and $(n,m)\in E$ iff $(n-m)\in A$ ($A\subseteq \mathbb{Z^d}$ is fixed), $\Omega(G)$ is a subshift of finite type.

Abstract: We present several new results concerning mixing properties of
hyperbolic systems preserving an infinite measure making a particular
emphasis on mixing for extended systems. This talk is based on a joint
work with Peter Nandori.

Abstract: A subset of the integers P is called predictive if for all zero-entropy processes X_i; i in Z, X_0 can be determined by X_i; i in P. The classical formula for entropy shows that the set of natural numbers forms a predictive set. In joint work with Benjamin Weiss, we will explore some necessary and some sufficient conditions for a set to be predictive. These sets are related to Riesz sets (as defined by Y. Meyer) which arise in the study of singular measures. This and several questions will be discussed during the talk.

Abstract: I will explain what measure distal transformations are
and describe some new constructions obtained with Eli Glasner.
These answer, inter alia, a question recently raised by Ibarlucia and Tsankov
concerning the existence of strongly ergodic non compact distal actions of the
free group.

Gibbs measures vs. random walks in negative curvature
The ideal boundary of a negatively curved manifold naturally carries two types of measures.
On the one hand, we have conditionals for equilibrium (Gibbs) states associated to Hoelder potentials; these include the Patterson-Sullivan measure and the Liouville measure. On the other hand, we have stationary measures coming from random walks on the fundamental group.

Abstract: We consider generic translation flows corresponding to Abelian differentials on flat surfaces of genus $g\ge 2$. These flows are weakly mixing by the Avila-Forni theorem. Recently Forni obtained Hoelder estimates on spectral measures for almost all translation flows, following earlier work by Bufetov and myself in genus two. Combining Forni's idea with our methods, we extended our proof to the case of arbitrary genus $g\ge 2$. It is based on a vector form of the Erd\H{o}s-Kahane argument, which I will try to explain.
This is a joint work with A. Bufetov.

Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism between any two such Brownian motions. For fixed h >0, we construct by elementary methods, isomorphisms with almost surely finite coding windows between Brownian motions reflected on the intervals [0, qh] for all positive rationals q. This is joint work with Terry Soo.

Abstract:
Recently Uri Gabor refuted an old conjecture stating that any
finitary factor of an i.i.d process is finitarly isomorphic to an
i.i.d process. Complementing Gabor's result,
in this talk, which is based on work in progress with Yinon Spinka,
we will prove that any countable-valued process which is admits a
finitary a coding by some i.i.d process furthermore admits an
$\epsilon$-efficient finitary coding, for any positive $\epsilon$.
Here an ``$\epsilon$-efficient coding'' means that the entropy

Abstract: In this talk, I'll show the invalidity of finitary counterparts for three main theorems in classification theory: The preservation of being a Bernoulli shift through factors, Sinai's factor theorem, and the weak Pinsker property. This gives a negative answer to an old conjecture and to a recent open problem.