Colóquios - Klein, Poincaré, and making sense of geometry at infinity

Klein, Poincaré, and making sense of geometry at infinity
Expositor: Rod Gover
Instituição: University of Auckland
Data e Horário: 28/03/2019 | 17:00 hs

Resumo: Non-compact spaces can be "too big" or awkward to deal with for many problems in mathematics. Making a space compact by adding points in some appropriate way is a classical notion known as compactification. In geometric settings these new points are typically "at infinity", in a suitable sense. Conformal compactification, as originally defined by Penrose, has long been recognised as a particularly effective framework in settings where analysis or physics is involved.

This generalises the treatment of infinity in the Poincaré model of hyperbolic space. It has recently emerged that conformal compactification can be recast in a way that places it as a special case in a very general “geometric compactification" picture. This has not only aesthetic appeal: the new interpretation comes automatically with tools that show how a space may be compactified and the same tools can also be used to make sense of the geometry at infinity and to concretely relate it to the asymptotic phenomena of the original space. This is based in part on joint work with Andreas Cap and Matthias Hammerl.