4:00 pm Thursday, September 21, 2017

Alan Haynes (University of Houston)

Abstract: In this talk we will begin with a brief history of the
mathematics of aperiodic tilings of Euclidean space, highlighting
their relevance to the theory of physical materials called
quasicrystals. Next we will focus on an important collection of point
sets, cut and project sets, which provide us with mathematical models
for quasicrystals. Cut and project sets have a dynamical description,
in terms of return times to certain regions of linear R^d actions on
higher dimensional tori. As an example of the utility of this point of
view, we will demonstrate how it can be used, in conjunction with
input from Diophantine approximation, to classify a subset of
`perfectly orderedâ€™ quasicrystals.