# Ian Morris: Continuity, computability and strict monotonicity of the affinity dimension

**Time:
**
Thu 2017-09-14 14.00 - 14.50

**Lecturer: **
Ian Morris, University of Surrey

**Location: **
Institut Mittag-Leffler, Auravägen 17, Djursholm

The affinity dimension, introduced by Falconer in 1988, is a non-conformal analogue of the similarity dimension which is defined for affine iterated function systems. I will discuss some elementary properties of the similarity dimension - namely, its continuity, computability and strict monotonicity - and describe recent work on the nontrivial matter of extending these properties to the affinity dimension. This will include a short description of my recent work on the equilibrium states of the singular value potential with Antti Käenmäki and Jairo Bochi.