Seminar

The focus of this talk is (families of) widely separated configurations of points in Euclidean space, and the analysis of certain associated elliptic operators.  Families of widely separated point configurations generally display `multi-scale' or equivalently `clustering’ behaviour. The different scales are the relative sizes of the lengths d(p_i, p_j) between the points in the configuration. We use blow-up techniques to resolve such families and to study certain associated Laplace-type operators.  The main result is a set-up in which these elliptic families can be inverted uniformly.  The motivation for this study is the construction of corners of the compactified moduli space of monopoles, and if time permits, this application will be briefly discussed.