PIMS Voyageur Colloquium: Ian Putnam

Abstract

In the 1960's and 70's, mathematical patterns in Euclidean space were discovered which displayed a high degree of order, but which were not periodic. Later, Daniel Shechtman found physical materials (quasicrystals) which can be modeled by such patterns. He was awarded the Nobel prize in chemistry for this discovery last year. In this talk, I will discuss the mathematical aspects of this theory. I will provide some examples and several constructions of aperiodic structures. The subject is notable for the range of mathematics which has been employed in their study and I will discuss how some ideas in topology provide new invariants and insights.