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Monday, February 08, 2016
4:00 PM - 5:00 PM

Noncommutative Geometry Seminar

II_1 Factors with Non-isomorphic Ultrapowers
Adrian Ioana, Professor, Mathematics, UCSD,

A II_1 factor is an infinite dimensional von Neumann algebra which has infinite center and admits a trace. As I will recall, examples of II_1 factors arise naturally from countable groups (with infinite conjugacy classes), and their measure preserving actions on probability spaces. I will present a recent result showing the existence of uncountably many separable II_1 factors whose ultrapowers, with respect to arbitrary ultrafilters, are pairwise non-isomorphic. More precisely, the families of non-isomorphic II_1 factors originally introduced by McDuff (1969) are such examples. This is joint work with Remi Boutonnet and Ionut Chifan.

For more information, please contact Farzad Fathizadeh by email at farzadf@caltech.edu or visit http://www.math.caltech.edu/~ncg/.