Deformation and Rigidity for von Neumann Algebras

In this talk I will give an overview of Popa’s deformation/rigidity theory for von Neumann algebra factors. The main motivation for this theory is the question of when an isomorphism of factors arising from group actions comes from an isomorphism of the groups. After providing some background on early results, examples of using deformation/rigidity to prove structural results will be given. Topics discussed in this talk include deformations, Cartan subalgebras, and intertwining of subalgebras.