Compactification, resolution and monopoles.
by Professor Richard Melrose
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.
For More Information: Paul Norbury tel: 8344 5534 email: P.Norbury@ms.unimelb.edu.au