In this talk we'll relate certain properties of discrete group actions to structural properties of the corresponding crossed product von Neumann algebras. In particular, we'll investigate the primeness of generalized wreath product II$_1$ factors using techniques from deformation/rigidity theory. We give general conditions relating tensor decompositions of generalized wreath products to stabilizers of the associated group action, and use this to find new examples of prime II$_1$ factors.

Bio: Gregory Patchell is a Canadian PhD candidate, currently studying under the supervision of Adrian Ioana at the University of California, San Diego. He completed his undergraduate in Pure Mathematics at the University of Waterloo. His research largely concerns the structural theory of von Neumann algebras, particularly II$_1$ factors.