Second Simon Norton memorial lecture

I went to London on Wednesday for the second in the series of Simon Norton memorial lectures, endowed by his family in memory of this remarkable mathematician.

The lecture was given by Leonard Soicher; I gave the first in the series last year. Here are the first two lecturers, with Yang He, the organiser of the series, in LIMS (in Michael Faraday’s rooms in the Royal Institution).

I don’t want to compare our lectures, but I will briefly contrast our approaches.

Leonard began, more or less, with the axioms for a group, and explained how groups describe symmetry (with an example, the projective plane of order 3, which came into his talk later). He then described some of the excitement of being around while the properties of the sporadic simple groups were being investigated (he was too late to take part in their discovery), and some of Simon’s technical work on the Monster.

On the other hand, I “explained” groups using the Rubik cube, and “explained” Norton algebras using the football. (Griess constructed the Monster as the group of symmetries of a Norton algebra in 196883 dimensions.)

This leads to a little puzzle. Of what is the group of the Rubik cube the symmetry group? I think this question does need a bit of thought, but I leave it to you.