Theatre B, Richard Berry Building
The University of Melbourne
Associate Professor Donald Taylor
School of Mathematics and Statistics
The University of Sydney
The Platonic solids are the epitome of symmetry and they lead to the study of reflection groups in Euclidean space. Their complex analogues introduce us to unitary reflections and hence to the study of finite unitary reflection groups. They were classified by Shephard and Todd in 1954. In two dimensions the groups are closely associated with the binary tetrahedral, octahedral and icosahedral groups. In higher dimensions many examples can be constructed via complex structures on the quaternions and octonions. This is a topic with a rich history, many recent results, and many open problems, all of which will be surveyed in this talk.