Event № 1148

We will give a short sketch of topological K-theory for compact spaces and explain its connection with K-theory for C*-algebras. Then we will state the theorems that are used for computing K_*(A \ltimes G) where G  is the integers or the reals, and for computing K_*(A\otimes B).  Finally, we will show how these tools have been used to solve outstanding conjectures of Kaplansky, Kadison, and to shed new light on the representation theory of certain classes of groups.