An Introduction to Equivariant Cohomology
It gives me great pleasure to start off this “anniversary” meeting, even if by default.
The 1970 summer school here at Les Houches was a very memorable event for me and my whole family and it is quite wonderful and magical to see, among the many young and eager faces, so many friends of old. In the nearly 30 years since 1970, I am very pleased to report that the dialogue between physiCs and mathematics has increased dramatically, and, on the mathematical side at least, this interaction has been highly productive. The Yang-Mills theory spawned the Donaldson invariants of four-manifolds, later to be augmented by the Seiberg- Witten invariants. Current algebras engendered a new and beautiful representation theory of Loop groups and Kac- Moody algebras. Knot theory has been reinvigorated by the “ChernSimons Theory,” while 19th century questions in algebraic geometry have been solved by methods initiated by “String Theory.” And, on a personal note, I might add that nowadays it is usually the Physics graduate students who are the stars in my geometry courses.
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