A Celebration of the Mathematical Legacy of Raoul Bott (CRM Proceedings & Lecture Notes)

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

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.