Modul: MAT075 Zurich Graduate Colloquium

## What is... a badly approximable number?

Roland Prohaska talk

**Date:** 10.12.19 **Time:** 17.15 - 18.30 **Room:**

Badly approximable numbers are irrational numbers whose rational approximations are, in some sense, as inefficient as possible. We will define them, give a survey of their basic properties, and present a dynamical characterization in terms of the geodesic flow on the space of unimodular lattices in the plane. Known as the Dani correspondence principle, this connection has recently been used to answer a good number of long-standing questions about badly approximable numbers, such as their prevalence on certain fractal sets.