BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Tutorial on von Neumann algebras Ioana, Adrian


In the first lecture, I will review basic notions and constructions of von Neumann algebras. The second lecture will be devoted to property Gamma and McDuffâ s property for II_1 factors. In the third lecture, I will discuss the isomorphism problem for ultrapowers of II_1 factors. ========== Lecture 1: Define vN algebras and state the bicommutant theorem. Introduce tracial vN algebras and the hyperfinite II_1 factor. Group and group measure space vN algebras. Lecture 2: Define property Gamma and discuss the connection with inner amenability of groups. Define McDuffâ s property. Examples of II_1 factors that are Gamma but not McDuff. Lecture 3: The ultrapower construction for tracial vN algebras. Discuss dependence on the choice of the ultrafilter and examples of II_1 factors with non-isomorphic ultrapowers.

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