Department of Mathematics
Title : Prolongation of overdetermined systems of PDE's in parabolic geometries
| Speaker: Josef Silhan Affiliation: Masaryk University Time: 1pm Friday, 9 September, 2011 Location: G08, 70 Symonds Street |
Abstract
| The class of parabolic geometrical structures covers in particular conformal and projective geometries but also certain contact structures (e.g. partially integrable CR structures) and other geometries. They can be considered as Cartan curved analogues of homogeneous spaces $G/P$ where $G$ is a semisimple Lie group and $P$ a parabolic subgroup. Among invariant operators there is a distnguished class of so called first BGG operators. Corresponding systems of PDE's are known to be overdeterminened. The aim of the talk is to describe prolongation of these systems, i.e. find an invariant linear connection whose parallel sections are in 1-1 correspondence with solutions. This problem turns out to be easy on homogeneous spaces $G/P$, but we shall present how to build invariant prolongation in on curved parabolic manifolds. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
