John Ryan
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SPECIAL MATHEMATICS COLLOQUIUM
Speaker: John Ryan Abstract. In this talk we will look at a number of first order differential operators that exhibit a certain degree of symmetry under angle preserving transformations. These are generally refered to conformal transformations. Such operators include the the Dirac operator on Euclidean space, and the Atiyah-Siger-Dirac operator on a spin manifold. We will show how the second operator is a natural generalization of the first. We shall also consider non-linear p and infinite Dirac operators and their conformal invariances. A generalization to a Hermitian setting will also be considered. Some applications will also be introduced. |