*S peaker.* Mark Pollicott

*Date.*25.10.22 at 3:30 pm

* Abstrac*t. We will consider 2 classical questions:

(a) Given an iterated function scheme of contractions (on the unit interval), what is the Hausdorff dimension of the limit set?

(b) Given a random product of finitely many matrices, what is the (largest) Lyapunov exponent?

We will motivate this by simple applications to (a) Number Theory; and (b) Euclidean and Hyperbolic Geometry.