Robert Yuncken: A groupoid approach to pseudodifferential operators
Robert Yuncken (Univ. Clermont-Ferrand II, France) will give a talk with title: A groupoid approach to pseudodifferential operators
Abstract: Connes introduced the "tangent groupoid" of a manifold as a geometric device for linking a classical pseudodifferential operator to its symbol, yielding a novel proof of the Atiyah-Singer index theorem. Since then, numerous variations on the tangent groupoid have been produced, each adapted to a different class of pseudodifferential operators. In this talk we will consider the reverse problem: associating to a given tangent groupoid a pseudodifferential calculus. We shall show that the kernels of classical pseudodifferential operators are precisely the essentially homogeneous fibrewise distributions on Connes' tangent groupoid. This leads to a natural pseudodifferential calculus of subelliptic type on a manifold with a filtration on its Lie algebra of vector fields.