Speaker
Gennadi Kasparov
(Vanderbilt University)
Description
In recent years there was a significant progress in the theory of pseudo-differential operators on filtered manifolds. I will introduce in my talk a wider class of manifolds which I call manifolds with a tangent Lie structure. I will explain a coarse approach to pseudo-differential theory which gives a simplified pseudo-differential calculus containing only operators of order 0 and negative order. This calculus easily leads to the Atiyah-Singer type index theorem for operators of order 0 on manifolds with a tangent Lie structure. For filtered manifolds this calculus agrees with the known H\"ormander and van Erp - Yuncken calculi, which allows to extend the index theorem to operators of any order.
https://sites.google.com/view/julgfest