For more information about this meeting, contact Nigel Higson, Stephanie Zerby, John Roe.

Title: | Operator spaces, representations of reductive groups, and a Kasparov product |

Seminar: | Noncommutative Geometry Seminar |

Speaker: | Nigel Higson, Penn State |

Abstract: |

This is joint work with Pierre Clare and Tyrone Crisp. Lafforgue gave a geometric proof of the Connes-Kasparov conjecture for real reductive groups (a representation-theoretic proof had previously been sketched by Wassermann) and in his 2002 ICM address he used this as the starting point for a new approach to Harish-Chandra's classification of the discrete series. The new approach requires the computation of some Kasparov products, which are fortunately easy because the underlying Hilbert spaces are finite-dimensional. It is interesting to attempt to extend Lafforgue's approach to limits of discrete series, since these account for the rest of the K-theory of the reduced group C*-algebra. But now the Kasparov products are more difficult, because among other things the underlying Hilbert spaces are infinite-dimensional, and are only geometrically defined as operator spaces (the Hilbert space structure requires the Plancherel theorem). |

### Room Reservation Information

Room Number: | MB106 |

Date: | 02 / 04 / 2016 |

Time: | 02:30pm - 03:30pm |