Claire Debord(Université Blaise Pascal)
Title: Blowup and deformation groupoids related to index problems
Abstract: A Lie groupoid G comes with its natural family of elliptic
pseudodifferential operators and the corresponding analytical index is
nicely described thanks to its adiabatic groupoid. We will be interested in
the situation where a sub-manifold V of the units space of G brings
singularity: it forces operators of G to slow down near V in the normal
direction and propagate along a sub-Lie groupoid of G inside V.This
behavior is nicely encoded in some Blowup groupoid.In this talk, we will
present natural constructions of Lie groupoids coming from deformation
and blowup procedure. These constructions enable one to recover many
known constructions of Lie groupoids involved in index theory and lead to
new index problems. This is a joint work with G. Skandalis.