Roger J. Plymen (University of Manchester)
roger@maths.man.ac.uk This will be an easy-listening talk on one of Alain Connes' elementary ideas, namely the replacement of the quotient X/G by the crossed product of C(X) by G, where X is a locally compact space and G is a locally compact group. The extended quotient is an intermediate idea. K-theory, cyclic theory and orbifold cohomology are part of the story. Representation theory furnishes some good examples: SL(2,R), the Bernstein centre, Langlands parameters for GL(n).