Graduate Seminar

Location:  ED 114

Speaker: Jeffery Xu

MSc Student supervised by Remus Floricel

Title:  Measurable Fields and Product Systems

 Abstract:

This talk serves as a continuation of my previous presentation. Previously we spoke of product systems of Hilbert spaces, a Borel measurable family of Hilbert spaces indexed over some Borel space. Clearly for bundle enthusiasts, this screams "vector bundle" and so it is. But product systems are much more than simply bundles as they require the notion of "trivialization" and a product between fibres. In essence, we are requiring that the Hilbert space fibres are the same (up to isomorphism of course), so the fibres do not get overly unwieldy. This leads us to measurable fields, of which product systems are special examples. The point of this talk is to continue further onward and consider a different mathematical category of objects, von Neumann algebras. We will see the analogous product systems of von Neumann algebras and how they relate to the aforementioned system of Hilbert spaces. To that end, we will develop measurable fields of von Neumann algebras in much the same way.