Scheme: Wolfson Research Merit Awards
Organisation: University of Warwick
Dates: May 2015-Apr 2020
Summary: The study of the long term behaviour of simple systems is a central theme in the field of dynamical systems. Professor Smillie’s research involves two such systems: polygonal billiards and complex dynamics in two dimensions.
Billiard trajectories in polygonal regions in the plane are easy to describe but the analysis of their long term behaviour leads to a range of interesting mathematical questions in seemingly unrelated areas of mathematics. One key tool is the idea of renormalisation, inspired by physics, in which one studies the effect of changing the time scale and the space scale.
The field of one dimensional holomorphic dynamics has developed into a beautiful area of mathematics with beautiful connections between dynamics and fractal geometry. Professor Smillie is investigating holomorphic systems in higher dimensions and connections with potential theory.