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Analysis SeminarExport this event to calendar

Friday, November 22, 2013 — 3:30 PM EST

Jon Bannon, Siena College

“Generic Weak Mixing and the Negation of Property (T)”

The various mixing properties studied in ergodic theory are expressible as flavors of asymp- totic independence which are initially difficult to distinguish from one another by the math- ematical naked eye. A result of P. R. Halmos from 1943 establishes that, if one topologizes measure-preserving transformations in a natural way, the set of weakly mixing transforma- tions is a dense Gδ subset. A subsequent result of V. Rokhlin in 1948 shows that in contrast with Halmos’s result, the strongly mixing transformations are nowhere dense. This surprising dichotomy, and an interesting technical result of G. Lorentz, led H. Dye to consider a more general notion of weak mixing for unitary representations of (amenable) topological groups. V. Bergelson and J. Rosenblatt subsequently obtained an analogue of Halmos’s original result in this new setting, where the acting group is amenable and locally compact and the role of Halmos’s topology is played by the Fell topology on unitary representations. Recently, D. Kerr and M. Pichot have proved that the analogue of Halmos’s result (genericity of weak mixing) holds precisely when the acting group fails to have Kazhdan’s property (T). In joint work with J. Cameron and S. White, we show that a perfect analogue of Kerr and Pichot’s result holds in the setting of finite von Neumann algebras and correspondences, thus providing another global characterization of property (T) for von Neumann algebras. In this lecture we will discuss the above story in a bit more detail, and present the skeleton of the proof of our result.

Location 
MC - Mathematics & Computer Building
5136B
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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