*** Please note that there is no evaluation for this course. If you wish to take this course for credit (as a reading course), you must arrange it with Professor Higson and your home university depart first. Unfortunately, we are unable to issue a Certificate of Participation for remote participants of this course unless arrangements are made prior. ***

Instructor: Prof. Nigel Higson
Email: ndh2@psu.edu

Course Dates: September 12th - November 30th, 2023
Mid-Semester Break: October 30th - November 3rd, 2023
Lecture Times: Tuesdays & Thursdays | 10:30 AM - 12:00 PM (ET)

Format: Hybrid - In Person at Room 210, Fields Institute | Remote via Zoom: https://zoom.us/j/96775594350

Course Description

The tangent groupoid is a geometric construction that can be applied to any smooth manifold. Alain Connes pointed out its relevance to the Atiyah-Singer index theorem, and ever since he did so the tangent groupoid has appeared regularly in noncommutative geometry, often in ways related to index theory but usually illuminating other issues at the same time. Good examples of this are the elegant and simple ways of understanding pseudodifferential operators that have been developed recently by Claire Debord and Georges Skandalis, and by Erik van Erp and Bob Yuncken. I shall start with pseudodifferential operators, then introduce the tangent groupoid through them, and go on to examine applications in representation theory, hypoelliptic partial differential equations and elsewhere.