Clifford Research Group

Seminars Academic year 2008-2009



Conformal structure, Dirac type operators and the p-Dirac equation
John Ryan (University of Arkansas, USA)

Abstract:
Clifford analysis is the study and application of Dirac operators and Dirac type operators in analysis and geometry. Such operators include, but are not limited to,  the Dirac operator in euclidean space, the conformal, or Yamabe, operator on the sphere and the Atiyah-Singer-Dirac operator on a spin manifold. All of these operators have a conformal covariance, whether it be under conformal transformations or conformal rescaling of a metric . We shall explore this conformal symmetry and the relations to various Laplacians. We shall concentrate on the non-linear p-Laplacian and infinite Laplacian and their corresponding non-linear Dirac equations, together with their conformal covariances. We shall deal with these covariances in euclidean space, the sphere and on spin manifolds.
Some of this work is joint work with Mike Eastwood, Craig Nolder and Tom Bieske.


Monogenic Functions on Surfaces
Heikki Orelma (Tampere University, Finland)

Abstract:
The aim of the lecture is to derive the Dirac equation on surfaces. The content of the talk will be: 1. Differential forms,
2. Monogenic differential calculus,
3. Clifford algebraic tools for surfaces,
4. Surface monogenics.
The lecture will be given as explicit and as elementary as possible.

Clifford Analysis and Electromagnetism - Part II
Ghislain Franssens (Belgian Institute for Space Aeronomy)

Tentatieve inhoud (in Dutch):
uitbreidingen van de CA
   - over pseudo-Euclidische ruimten
   - over pseudo-Riemann ruimten
   - situering van toepassingen in een (eventueel uitgebreide) CA
   - overzicht van de moeilijkheden die optreden bij formulering van deze uitbreidingen en   
     suggesties om ze aan te pakken,
   - specifieke toepassing: EM boundary value problem in a given gravity field
   - conclusies

Clifford Analysis and Electromagnetism - Part I
Ghislain Franssens (Belgian Institute for Space Aeronomy)

Tentatieve inhoud (in Dutch):
   - motivering: via Electromagnetisme (EM) naar Clifford Analyse (CA)
   - wiskundige interpretatie van het EM / electromagnetische interpretatie van de CA
   - overzicht van het uit te voeren project
   - geassocieerde homogene distributies (AHDs) (speciale gevallen: scalaire, Cauchy
     en Hilbert kernels)
   - convolutie en vermenigvuldigingsalgebra voor AHDs
   - bespreking van belangrijkste resultaten tot nu toe (o.m: afleiding kernels)
   - conclusies

Department of Mathematical AnalysisDepartment of Mathematical Analysis