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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Aperiodic Order: dynamical systems and diffraction
SPEAKER:Robert V. Moody (University of Alberta and BIRS)
DATE:Jeudi, 9 Octobre 2003
TIME:3:00 pm
ROOM:KED B005
ABSTRACT:

Real life quasicrystals have the distinction of being pure point diffractive yet not periodic. At the time of their discovery in 1984 such structures were thought to be impossible, and even within mathematics they were not anticipated. Since then a large number of quasicrystal types (of remarkable perfection) have been formed experimentally and at the same time considerable progress has been made on the mathematical understanding pure point aperiodic structures.

In this lecture we will show some of the ways that mathematicians and physicists have modeled such structures. One of these methods is based on projection from higher dimensional spaces, a concept that in spite of its usefulness has often bothered physicists. We will show how that to a large extent pure point diffractivity forces this type of model. Key ingredients in this are the use of measure-theoretical dynamical systems and almost periodic measures.

The subject is ultimately a chapter in discrete geometry. It is quite accessible and lends itself very well to nice pictures. The talk will be aimed at a general mathematical audience.

About the speaker. Professor Robert Vaughan Moody, FRSC, is one of the most outstanding Canadian mathematicians of our days. Born in Great Britain in 1941, he graduated with B.A. (Mathematics) from the University of Saskatchewan in 1962, and received both his M.A. (Mathematics) and PhD from the University of Toronto in 1964 and 1966, respectively. His many honours include the 2000 Order of Canada, the 1994-96 Eugene Wigner Medal, and the 1998 CRM/Fields Institute Prize.

Professor Moody's research is concerned with different aspects of symmetry. He has given his name to one of the best-known objects of today's mathematics and mathematical physics, the Kac-Moody algebras. These are proper infinite-dimensional analogues of classical simple Lie algebras, discovered independently by Robert Moody and by Victor Kac. By now Kac-Moody algebras play a fundamental role in mathematics and theoretical physics. There are at least fifteen hundred published mathematical articles investigating and using Kac-Moody algebras, and many more physical ones.

Since about a decade ago, Professor's Moody main research interests have shifted to aperiodic orders and quasi-crystals, which is a remarkable area of applications of mathematics. His lecture will be of considerable interest to a great many scientists in a diverse variety of disciplines.

For more information, visit Professor Moody's home page