Series: Mathematics Colloquium

Date: Thursday, April 22, 2004

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Hosts: Augustin Banyaga, Paul Baum

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Aderemi Kuku, Institute for Advanced Study

Title: 

  A Complete Formulation of the Baum-Connes Conjecture for the Action
  of Discrete Quantum Groups

Abstract:  

  The goal of this talk is to present a formulation of the Baum-Connes
  conjecture for the action of discrete quantum groups and test the
  conjecture with some examples.  The talk starts with an explanation
  of the philosophy behind the classical formulation of the conjecture
  in terms of group actions and the rationale for the new formulation
  in terms of quantum group actions.  Next we provide definition of
  the basic notions involved in the classical formulation of the
  conjecture -- full and reduced group C*-algebras, K-theory and
  K-homology for C*-algebras, proper group actions, universal space
  for proper actions, assembly maps -- leading to the classical
  formulation of the conjecture.  We also briefly review the current
  state of knowledge on the conjecture.  Next we define quantum
  analogues of the notions above -- discrete quantum groups, A, say,
  equivariant and proper A-actions, A-equivariant K-theory and
  K-homology, assembly maps, etc., culminating in the new formulation
  of the conjecture.  Finally we state the results obtained by testing
  the new conjecture with some examples.