## CRM/Fields Institute Prize

### Public Lecture Given by Robert V. Moody, *University
of Alberta*

### What is Aperiodic Order?

*Thursday, September 24, 1998 – 4:00 p.m.*

**Abstract:** In the natural world we are surrounded
by large highly ordered structures that are assembled out of minute
entities (atoms). How Nature accomplishes this is largely unknown. The
simplest and by far the most common system is the periodic repetition
of some basic motive. These are crystals. We now know that there are
solid-state materials that are crystallographic in almost every way,
including long-range order that rivals in perfection with that found
in crystals, which are most definitely not periodic. In this lecture,
we will discuss some of the mathematics that is being used to model
these quasi-crystals, its unexpected origins, and the lovely way in
which it weaves together various diverse disciplines of mathematics.

**Robert
V. Moody** received his Ph.D. in 1966 from the University of Toronto.
He was elected to the Royal Society of Canada in 1980 and was awarded
the 1994-95 Eugene Wigner Medal (jointly with V. Kac) for "work on affine
Lie algebras that has influenced many areas of theoretical physics".

He was twice honoured by the Canadian Mathematical Society, first in
1978 when he was invited to present the inaugural Coxeter-James Lecture,
given to the most outstanding young Canadian mathematician within ten
years of their degree, and in 1995 when he was selected for the Jeffery-Williams
Prize Lecture for the 50^{th} Anniversary of the Canadian Mathematical
Society.

His discovery, independently from and simultaneously with V.G. Kac,
of an enormous new class of infinite dimensional Lie Algebras, which
are now called Kac-Moody algebras, is considered as one of the seminal
events in the history of mathematics in the last half of the twentieth
century. In recent years, with various collaborators Dr. Moody has been
studying the mathematical aspects of long-range aperiodic order, especially
the quickly emerging area of quasi-crystals.