|Laboratoire de Mathématiques Emile Picard
Institut de Mathématiques de Toulouse CNRS UMR 5219
Université Paul Sabatier
|Research axes of the Center Cairos||
W. K. Clifford: (1845-1879) was not only a genius mathematician but also a physicist and a philosopher.
(A) Using Cliffordian methods study: the five types of exceptional simple Lie algebras and the corresponding associated Lie groups; the singular Lie algebra D4 associated to O(8) and Spin(8); simple exceptional Jordan algebras; exceptional projective Moufang planes and non-associative composition algebras and applications to the foundations of quantum mechanics, quantum computing and cosmological models.
(B) Applications of triple systems to the study of bounded symmetric domains; relations to conformal geometry over classical pseudo-Euclidean spaces..
(C) Conformal spinors and generalized twistors; application to prequantization and quantization;
(D) Study of other spinorial algebras (Clifford-Heisenberg and orthosymplectic ones).
(E) Dirac operators on manifolds and their generalizations; new topics about Clifford analysis.
(F) Applications of Clifford algebraic methods in physics and engineering, in particular: multidimensional field theoretical models, robotics, control, image processing.
(G) Epistemological heritage of William Kingdom Clifford.
Last updated 1 June, 2007