Emanuel A. Lazar, University of Pennsylvania

Abstract:
Many systems in our everyday lives can be abstracted as large sets of points in space -- the Milky Way galaxy, the coffee in your mug, and the aluminum housing of your iPhone can all be viewed as large collections of point-like objects.  Understanding how these points are arranged is thus an interesting and natural problem, though aside from perfect crystals and ideal gases, describing this structure can be a very thorny problem.  We present a unified framework for characterizing local structure in ordered and disordered point systems; this framework is built on a semi-algebraic stratification of a relevant configuration space by the complete topology of a particle’s Voronoi cell.  Some relevant theorems, as well as applications to computational materials science, are considered.