Operator K-theory and the harmonic analysis of reductive symmetric spaces, 2
Speaker: Nigel Higson, Penn State
Abstract: These will be informal and introductory lectures about the K-theory perspective on the harmonic analysis of reductive symmetric spaces. In fact this perspective doesn’t exist yet, but it might soon. The philosophers teach us that when we study harmonic analysis on a (real reductive) group G, as Harish-Chandra did in his Plancherel theorem, we should consider G as a symmetric homogeneous space, namely the quotient of G times G by its diagonal subgroup. But when we study harmonic analysis on G from the operator K-theory perspective, as Connes and Kasparov did, we don’t follow the philosophers at all, and for that reason it is difficult to see how to extend the Connes-Kasparov theory to general symmetric spaces. I shall try to examine the prospects for a resolution of this puzzle.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm