Cartan Geometries and Invariant Multilinear Differential Operators

Jens Kroeske (ThinkTank Maths)

Monday 2nd March, 2009 16:00-17:00 Mathematics Building, room 204

Abstract

For a differential operator in Euclidean space (or better on the sphere) the notion of being invariant under conformal transformations is well understood. Recent research has extended this notion for linear differential operators to conformal manifolds and more generally to a wide class of Cartan Geometries. The classification of such invariant linear differential operators has led to many interesting results. This talk will give a brief introduction to the concept of Cartan Geometries, the general notion of invariance and motivates the study of multilinear differential operators. General classification results and the ideas behind it that go back to Penroses Twister Theory will be presented.

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