Title:  Dynamics, C*-algebras, and K-theoretic rigidity
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Abstract:  Dynamics provides some of the most interesting and ubiquitous
examples in the theory of operator algebras.  It is typically difficult,
however, to understand their fine structure.  A conjecture of Elliott
(c. 1990) predicts that the C*-algebras associated to minimal dynamical
systems on compact metric spaces (among others) will be classified up to
isomorphism by their K-theory and tracial state spaces.  In the case of
uniquely ergodic systems, K-theory alone should suffice.

In this talk I will explain how characteristic class obstructions can
be used to prove that the conjecture can only hold for metric spaces of
finite covering dimension.  Modulo this necessary condition, I will
present the solution of Elliott's conjecture in the uniquely ergodic
case.  (Joint work with Wilhelm Winter.)