The geometry of Markov diffusion generators

Ces notes sont un resume d'un mini-cours presente a l'Ecole Polytechnique Federale de Zurich en novembre 1998. Elles ont pour but d'exposer quelqu'unes des idees geometriques de l'etude des generateurs de diffusion developpees par D. Bakry et ses collaborateurs au cours des dernieres annees. Les notions abstraites de courbure et dimension, qui etendent les definitions geometriques, sont mises a profit dans des demonstrations fonctionnelles de theoremes de comparaison riemanniens. Constantes optimales et modeles de reference forment un aspect essentiel de l'analyse. Ces notes, qui pour l'essentiel ne comportent pas de demonstrations, se proposent de decrire les grandes lignes et les principes generaux de cette etude.

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