Fall 2007

## September 4 |
## Tom Kriete## Introduction to K-theory for C*-algebrasThis series of talks, with various speakers, will continue for much of the year as the schedule permits. Lectures on other topics, both in-house and by visiting speakers, will be interspersed throughout. |

## September 11 |
## David Sherman/Tom Kriete## Introduction to K-theory for C*-algebrasNotes from the first two seminars |

## September 18 |
## Tom Kriete## Introduction to K-theory for C*-algebrasNotes |

## September 25 |
## Katie Quertermous/Tom Kriete## Introduction to K-theory for C*-algebrasNotes |

## October 2 |
## Tom Kriete## Introduction to K-theory for C*-algebrasNotes |

## October 9 |
No meeting (reading day) |

## October 16 |
## Tom Kriete## Introduction to K-theory for C*-algebrasNotes |

## October 23 |
## David Sherman## Why operator spaces? / Introduction to K-theory for C*-algebras(first half) I'll introduce operator spaces and hopefully give some idea why they're interesting. This is intended to prep the audience for Zarikian's talk Nov. 13, and it may all be review for attendees of Tom's course last semester.(second half) I'll introduce the dimension semigroup of a C*-algebra, then explain the Grothendieck construction which leads to K_{0}.
Notes |

## October 30Kerchof 326 |
## Brent Carswell, Allegheny College## Conditional expectation, Bergman projection, and disintegration of Lebesgue area measure
Aleksandrov proved that on the space L |

## November 5 (Monday)3:30 PMKerchof 205 |
## Pietro Poggi-Corradini, Kansas State University (visiting George Mason University)## Some new versions of Schwarz's lemma using diameters, capacity and areaWe first recall Schwarz's lemma and its generalization using diameter given by Landau and Toeplitz in 1907. We then give a new proof of this result which allows to use higher diameters and even capacity. Time permitting we will sketch what happens when using area and we will state some open problems. This is joint with Bob Burckel, Don Marshall, David Minda, and Tom Ransford. Notes |

## November 13Kerchof 326 |
## Vrej Zarikian, U.S. Naval Academy## Operator spaces, multipliers, and applicationsAfter a brief review of operator space theory we will discuss left multipliers of operator spaces, as introduced by Blecher. These are linear maps on the operator space which in some concrete representation of the operator space become left multiplication by a fixed operator. We then present a fundamental theorem of Blecher, Effros, and the speaker which characterizes left multipliers abstractly (i.e. without reference to a concrete representation of the operator space). As applications we give elegant proofs of the Blecher-Ruan-Sinclair characterization of unital (non-self-adjoint) operator algebras and a Banach-Stone theorem for such algebras. Time permitting, we indicate how one-sided multiplier theory leads to a one-sided M-ideal theory for operator spaces, analogous to the (two-sided) M-ideal theory of Banach spaces introduced by Alfsen and Effros in the 1970s. Slides from the talk, including a proof |

## November 20 |
No meeting (Thanksgiving week) |

## November 30 (Friday) |
## David Blecher, University of Houstoncanceled due to illness |

## December 4 |
## David Sherman## Greatest hits of C*-algebraic K-theoryNext semester Tom Kriete and I plan to lead a working seminar on this topic, based on Rordam's book. In this talk I will try to give some idea of the main objects, the main theorems, and what can be done with them. I will snobbishly ignore details and may even lie a little. Like any short compilation, this will be woefully incomplete -- interested parties should buy the boxed set in the spring! |

You can reminisce about previous semesters at the links below:

Spring 2007 Fall 2006 Spring 2006 Fall 2005 Spring 2005 Fall 2004 Spring 2004 Fall 2003 Spring 2003 Fall 2002