Abstract
In logic and computer science one often studies the complexity of decision problems. In mathematical logic this leads to the program of study of relative complexity of isomorphism problems and determining various complexity classes. Broadly speaking, a problem p in a class C is complete in C if any other problem in C reduces to p. The isomorphism problem for separable C^*-algebras has been studied since the 1960's and evolved into the Elliott program that classifies C^*-algebras via their K-theoretic invariants. During the talk I will discuss the complexity of the isomorphism problem for separable C^*-algebras and its completeness in the class of orbit equivalence relations.