Title: W*-superrigidity
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Abstract:  Given a free, measure preserving action of a countable group on a probability space, Murray and von Neumann constructed a finite von Neumann algebra known as the group-measure space construction. Properties of this von Neumann algebra reflect properties of the group action, however, in general much of the information about the group action is lost when passing to the von Neumann algebra.  For instance, a seminal result of Connes shows that any two free, ergodic actions of infinite amenable groups give rise to the same von Neumann algebra.  Recently, examples of group actions have been found such that the group-measure space construction completely remembers the group and the action.  Such actions are termed W*-superrigid, and we will present an overview of results in this direction.