For more information about this meeting, contact Nigel Higson.

Title: | C*-algebras beyond set theory |

Seminar: | Noncommutative Geometry Seminar |

Speaker: | Klaas Landsman, Radboud Universiteit Nijmegen |

Abstract: |

For reasons independently arising in constructive functional analysis and in the foundations of quantum physics, C*-algebras have been defined and studied in so-called Grothendieck toposes. These are categories of sheaves, which generalize the category of sets and functions on which standard mathematics is based, but whose intrinsic logic is intuitionistic (a Dutch specialty!). In particular, Gelfand duality holds in this generalized setting, though reformulated in such a way that the Gelfand spectrum of a commutative C*-algebra is defined constructively (i.e, as a so-called locale). So far, the main example of this generalized Gelfand theory has been the so-called Bohrification of an "ordinary" C*-algebra (i.e., defined in set theory). Our construction also leads to new questions about "ordinary" C*-algebras. This talk intends to give an overview of this entire development. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 09 / 01 / 2011 |

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