Abstract:

The starting point of this talk is the following general question: 

Suppose that X and Y are structures (C*-algebras, Boolean algebras, groups,...) and that Φ is an isomorphism between their quotients. Under what conditions can Φ be lifted to a homomorphism between X and Y?

Surprisingly, fairly general and natural conditions, in combination with nontrivial set-theoretic assumptions suffice. The methods used in lifting results of this sort combine set theory (forcing axioms) and Ulam-stability in the appropriate categories.

Bio-Sketch:

Professor Ilijas Farah is a Research Chair on Foundations of Operator Algebras at York University, Toronto. He is best known for his work on applying set theory and model theory to operator algebras and vigorously promoting the subject. He was an invited speaker at the 2014 ICM in Seoul.