**CRM Proceedings & Lecture Notes**

Volume: 50;
2010;
403 pp;
Softcover

MSC: Primary 01; 18; 19; 35; 55; 57; 58; 81;

Print ISBN: 978-0-8218-4777-0

Product Code: CRMP/50

List Price: $125.00

Individual Member Price: $100.00

**Electronic ISBN: 978-1-4704-1584-6
Product Code: CRMP/50.E**

List Price: $125.00

Individual Member Price: $100.00

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# A Celebration of the Mathematical Legacy of Raoul Bott

Share this page *Edited by *
*P. Robert Kotiuga*

A co-publication of the AMS and Centre de Recherches Mathématiques

A five-day conference celebrating the legacy
of Raoul Bott was held at the CRM on June 9–13, 2008. The
conference focused on the extraordinary impact Bott had on both
topology and interactions between mathematics, physics and technology.
The conference was co-organized by the Clay Mathematics Institute and
had support from the National Science Foundation (Award
0805925). Montreal was a natural venue for such an event since Raoul
Bott obtained two degrees in electrical engineering at McGill
University in the 1940s and an honorary doctorate from McGill in
1987. The fact that Bott's presence is still fresh in the minds of all
those involved made for a tremendous amount of enthusiasm and every
attempt has been made to channel this energy into this book.

The contributions to this book come from three generations of Bott's
students, coauthors, and fellow kindred spirits in order to cover six
decades of Bott's research, identify his enduring mathematical legacy and
the consequences for emerging fields. The contributions can be read
independently. In order to help a whole to emerge from the parts, the book
is broken into four sections and to make the book accessible to a wide
audience, each section starts with easier-to-read reminiscences and works
its way into more involved papers.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## A Celebration of the Mathematical Legacy of Raoul Bott

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Dedication x11
- Invention xi12
- Introduction 114
- Montréal, the 1940s, and mathematical prehistory 720
- My parents’ Montréal years and growing up with Raoul as my father 922
- Raoul Bott, McGill, the 1940s 1326
- Iron rings, Doctor Honoris Causa Raoul Bott, Carl Herz, and a hidden hand 1730
- The Bott–Duffin synthesis of electrical circuits 3346
- Early students and colleagues 4154
- Raoul Bott as we knew him 4356
- Working with Raoul Bott: From geometry to physics 5164
- The algorithmic side of Riemann’s mathematics 6376
- Actions of Lie groups and Lie algebras on manifolds 6982
- PDE from the point of view of multiplier ideals 7992
- Dirac operator and 𝐾-theory for discrete groups 97110
- The Lefschetz principle, fixed point theory, and index theory 109122
- A new look at the theory of levels 125138
- On the space of morphisms between Étale groupoids 139152
- Localization, equivariance and outgrowths of Morse theory and periodicity 151164
- Raoul Bott as we knew him 153166
- Loop products on connected sums of projective spaces 161174
- Equivariant cohomology and reflections 177190
- Connectedness of level sets of the moment map for torus actions on the based loop group 181194
- Computing characteristic numbers using fixed points 185198
- From minimal geodesics to supersymmetric field theories 207220
- Dualities and interactions with quantum field theory 275288
- Raoul Bott as my math teacher 277290
- A physics colloquium at McGill that changed my life 279292
- Geometric Langlands from six dimensions 281294
- Duality and equivalence of module categories in noncommutative geometry 311324
- Generalized complex geometry and T-duality 341354
- Topological quantum field theories from compact Lie groups 367380
- Back Cover Back Cover1418

#### Readership

Undergraduates, graduate students and research mathematicians interested in the life and work of Raoul Bott.