Symmetry is pervasive in both nature and human culture. The notion of chirality (or ‘handedness’) is similarly pervasive, but less well understood.
In this lecture I will talk about a number of situations involving discrete objects that have maximum possible symmetry in their class, or maximum possible rotational symmetry while being chiral.
Examples include graphs (networks), maps (graphs embedded on surfaces), compact Riemann surfaces (equivalence to algebraic curves), and polytopes (abstract geometric structures).
In such cases, maximum symmetry can often be modelled by the action of some universal group, the non-degenerate quotients of which are the symmetry groups of individual examples. The use of computational systems (like MAGMA) can be very helpful in producing examples, and then revealing patterns among them, or providing answers to various questions.
An intriguing question in some of these situations is about the prevalence of chirality: among small examples, how many are reflexible and how many are chiral? and what happens asymptotically?
At 2:30pm on the same day, also at the University of Sydney, Prof. Peter Sarnak (Princeton), the 2011 Mahler Lecturer, will give a Colloquium as part of his Mahler tour.