Noncommutative Geometry Seminar

Date: March 25, 2025

Time: 4:00PM - 5:00PM

Location: BLOC 605AX

Speaker: Gennadi Kasparov, Vanderbilt University

Title: Index theory on manifolds with a tangent Lie srtructure

Abstract: In recent years there was a significant progress in the theory of pseudo-differential operators on filtered manifolds. In my talk I will introduce 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 Hormander and van Erp - Yuncken calculi, which allows to extend the index theorem to operators of any order.