# Compactification, resolution and monopoles.

#### by Professor Richard Melrose

Institution: Massachussetts Institute of Technology
Date: Wed 16th March 2005
Time: 11:00 AM
Location: Russell Love Theatre, Richard Berry Building, The University of Melbourne

Abstract: One of the analytic reasons for considering compactifications
of non-compact manifolds is that it introduces natural classes of
functions which are smooth up to infinity\'. I will describe various
compactifications of Euclidean spaces using elementary constructions,
such as sterographic projection and polar coordinates (i.e. blow up).
These lead to related configuration spaces\' for particles and I will
describe how these in turn are related to the regularity of objects
such as the Newtonian potential. Then I will indicate how such spaces
lead to regularity properties for metrics on non-compact spaces and to
compactifications of moduli spaces for magnetic monopoles and so to
regularity results for the natural metrics on them.