Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Description
Instructor: Prof. Nigel Higson
Course Dates: September 12th - November 30th, 2023
Mid-Semester Break: November 20th - 24th, 2023
Lecture Times: Tuesdays & Thursdays | 10:30 AM - 12:00 PM (ET)
Format: Hybrid - In Person at Room 210, Fields Institute | Remote via Zoom
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.
Schedule
| 10:30 to 12:00 |
Lecture 01 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 02 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 03 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 04 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 05 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 06 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 07 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 08 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 09 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 10 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 12 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 13 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 14 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 15 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 16 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 17 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 18 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 19 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 20 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 21 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
| 10:30 to 12:00 |
Lecture 22 | Graduate Course on the Tangent Groupoid in Noncommutative Geometry
Nigel Higson, The Pennsylvania State University |
