We trace briefly the history of the Cuntz semigroup as an invariant for C*-algebras, from its beginnings as a natural carrier for dimension functions to its modern applications to the structure and classification of C*-algebras. We then turn to two recent results which involve the Cuntz semigroup in a crucial role, one related to existence of *-homomorphism in the non-nuclear setting and the other on the contractibility of Cuntz equivalence classes in Z-stable C*-algebras. This is joint work with Hao Wan and Chrisil Ouseph.
This seminar will take place at Queen's University Belfast, in MAPTC room 0G.017.
