Locally compact groups and von Neumann algebras

Von Neumann algebra theory is a branch of functional analysis dealing with weakly closed algebras of bounded operators on a Hilbert space and was developed by Murray and von Neumann in the 1940s, in order to put quantum mechanics into a solid mathematical framework. The most fundamental families of von Neumann algebras arise from a crossed product type construction, starting from actions of groups. Thanks to Sorin Popa's deformation/rigidity theory, enormous progress has been made over the last ten years in the classification of von Neumann algebras given as crossed products by countable groups. The main objective of this research project is to establish similar results for crossed products by locally compact groups. A particular focus will be on the uniqueness problem for Cartan subalgebras in these typically infinite factors.