April 21, 2024

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 50th 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.