Event № 129
In 1982, the Technion physicist Dan Shechtman verified the existence of physical quasicrystals via diffraction experiments - an observation for which he was awarded the Nobel prize in chemistry in 2011.In the past decades, mathematical diffraction theory evolved into a beautiful and rich research topiccombining various disciplines such as functional analysis, fourier analysis and ergodic theory.
This talk introduces the notion of autocorrelation for Delone sets in locally compact groups in terms of dynamical systems.A formula involving the Siegel transform is derived. To draw the connection to the classical theory, we stick to theframework of abelian groups giving rise to a uniquely ergodic dynamical system. Using the uniform ergodic theorem,it is shown that the (unique) autocorrelation measure coincides with the classical notion via a Folner limit ofnormalized difference Dirac combs. We conclude the talk by defining the diffraction measure as the Fouriertransform of the autocorrelation measure.