Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Computability of some matrix growth invariants arising in fractal geometry

Dr. Ian Morris talk

**Date:** 04.03.19 **Time:** 14.00 - 15.00 **Room:** ETH HG G 43

The dimension theory of self-similar sets without overlaps (which includes familiar examples of fractals such as the von Koch curve and Sierpinski gasket) was resolved essentially completely in the early 1980s. The dimension theory of their non-conformal relatives, self-affine sets, has by contrast been a source of stubborn open problems for over three decades. In this talk I will discuss a dimension formula for self-affine sets introduced by Falconer in the 1980s and describe a proof that the dimension value predicted by this formula is theoretically computable in a precise sense. As a by-product this argument also yields a new proof of the continuity of the affinity dimension, a result previously established by Feng and Shmerkin in 2014.