Abstract: A Thurston map is a branched covering map on a topological 2-sphere for which the forward orbit of each critical point under iteration is finite.  Each such map gives rise to a fractal geometry on its underlying 2-sphere. The study of these maps and their associated  fractal structures links diverse  areas of mathematics such as dynamical systems, classical conformal analysis, hyperbolic geometry, Teichmüller theory,  and analysis on metric spaces.  In my talk I will give an introduction to this area and report on some recent developments.

Short Bio: Mario Bonk received his academic education in Germany and obtained his PhD in 1988. He was Professor at the University of Michigan 2002–2010. Since 2010 he has been a Professor at the University of California, Los Angeles. His research lies at the interface of geometry and analysis and often relies on an extension of classical results to a non-smooth or fractal setting. He has (co)-authored more than 60 research publications, including a research monograph on "Expanding Thurston maps".  He was an invited speaker at the International Congress of Mathematicians (ICM) in 2006.