Clustering and Dispersion of Points in the Line and the Plane

There are many fundamental problems concerning sequences of points in $R^d$ that arise in various areas of mathematics and computation. Typical problems include finding or avoiding patterns, testing or validating various `random-like? behavior, and analyzing or comparing different statistics, for example. In this talk, we will examine various notions of clustering and dispersion for sequences in $R^d$. We will describe some recent results and mention numerous open problems.