I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

A dimension gap for continued fractions with independent digits (after Kifer, Peres and Weiss)

I'll report on recent applications of the LLL to two problems in the dynamics of general countable groups. The first concerns the existence of free symbolic minimal actions; the second asks about realizations of URS's (uniformly recurrent subgroups) as stability systems. I'll then concentrate on a solution of Gabor Elek to the second problem in the case of finitely generated groups.

Given a probability measure mu on the space of 2x2 matrices, there is, under mild conditions, a unique measure nu on the space of lines which is stationary for mu. This measure is called the Furstenberg measure of mu, and is important in many contexts, from the study of random matrix products to recent work on self-affine sets and measures. Of particular importance are the smoothness and dimension of the Furstenberg measure. In this talk I will discuss joint work with Boris Solomyak in which we adapt methods from

Abstract: I will describe joint work in progress with Aaron Brown, Federico Rodriguez-Hertz and Simion Filip. Our aim is to find some analogue, in the context of smooth dynamics, of Ratner's theorems on unipotent flows. This would be a (partial) generalization of the results of Benoist-Quint and my work with Elon Lindenstrauss in the homogeneous setting, the results of Brown and Rodriguez-Hertz in dimension 2, and the my results with Maryam Mirzakhani in the setting of Teichmuller dynamics.

A minimal representative for a dynamical system is a system that has the simplest possible dynamics in its topological equivalence class. This is very much related to "dynamical forcing": when existence of certain periodic orbits forces existence of others. This is quite useful in the analysis of chaotic systems. I'll give examples of minimal representatives in dimensions one two and three. In dimension three, I'll show that the minimal representative for the chaotic Lorenz equations (for the correct parameters) is the geodesic flow on the modular surface. This will be an introductory talk.