In this talk, we are going to talk about the topology of the moduli space of translation surfaces. These are closed Riemann surfaces with a flat metric on the complement of some finite number of points, around which the metric is given by cyclically…

# Categoria evento: Dynamical Systems Seminar

## Rational approximations to linear subspaces – Nicolas de Saxcé (CNRS, Université Paris-Nord 13)

Dirichlet’s theorem in Diophantine approximation implies that for any real x, there exists a rational p/q arbitrarily close to x such that |x-p/q|<1/q^2. In addition, the exponent 2 that appears in this inequality is optimal, as seen for example by…

## The Markoff spectrum on the Hecke group – Dong Han Kim (Dongguk University)

We consider the Markoff spectrum on the Hecke group. The Markoff spectrum on H4 is known as the Markoff spectrum of index 2 sublattices by Vulakh and the Markoff spectrum of 2-minimal forms or C-minimal forms by Schmidt, who characterized the…

## Continued fraction expansions of algebraic power series over a finite field – Yann Bugeaud (Université de Strasbourg)

Almost nothing is known on the continued fraction expansion of an algebraic real number of degree at least three. The situation is different over the field of power series Fp((x−1)), where p is a prime number. For instance, there are algebraic power…

## Irrational numbers and where to find them – Simon Kristensen (Aarhus University)

While all but countably many real numbers are irrational (and even transcendental), it is preciously difficult to decide whether this is the case for concrete real numbers, unless some special reason is apparent. For instance, we all know…

## Mixing of simple symmetric random walks on the circle – Klaudiusz Czudek (IST, Austria)

Fix an irrational number $\alpha$ and a smooth, positive, real function $p$ on the circle. A particle at a point $x$ in the circle jumps to $x+\alpha$ with probability $p(x)$ or to $x−\alpha$ with probability $1−p(x)$. In 1999 Sinai investigated…

## Shrinking-Target Problems and the Injectivity Radius Function – Reynold Fregoli (UZH)

In this talk, I will discuss a shrinking target problem in the space of uni-modular lattices, with target located at infinity and shrinking neighbourhoods determined by the injectivity radius function. This problem is connected to a large body of…

## Upper bound on the regularity of Lyapunov exponents of random product of matrices – Jamerson Bezerra (Nicolaus Copernicus University)

The study of the regularity of the Lyapunov exponent of random products of SL2(R) matrices is a rich subject with many important contributions in the past years. It is well established in the literature that the function which associates each finite…

## Random iteration on hyperbolic Riemann surfaces – Marco Abate (University of Pisa)

In this talk we shall describe the asymptotic behaviour of sequences of functions obtained by iteratively left-composing or right-composing holomorphic self-maps of a hyperbolic Riemann surface $X$. We shall consider in detail two cases: when the…

## Strong limit theorems for infinite measure-preserving dynamical systems with applications to non-standard continued fraction algorithms – Tanja Schindler (Univ. of Wien)

Aaronson’s theorem states that if we have a non-integrable observable over a finite measure system or if we have an integrable observable over a infinite measure space, then in both cases we can not have a strong law of large numbers. However -…