Séminaire de Géométrie et Quantification
Lundi 23 octobre 15h30 salle 201, IHP
Titre: “Equivariant algebraic index theorems and their applications to analysis”
Résumé : The general idea of index theorem is to compute the pairing of K-theory and K-homology in differential geometric/topological terms. Deformation quantisation enters the subject via various symbol calculi which allow one to study the associated pairings in terms of cyclic theory of the symbol algebras. The term “the algebraic index theorem” stands for the result of this (microlocal) computation. We will explain the structure of algebraic index theorems for algebras associated to the symbol calculi of certain classes of Pseudodifferential / Fourier Integral Operators. The latter (FIO) case corresponds to equivariant case of formal deformation quantisation. We will also sketch the path to the proof of the algebraic index theorems in both non-equivariant and equivariant context.