Course Description and Grading BreakdownCourse Meeting Time and LocationTuesday and Thursday 10:30 - 11:55 am 122 Math Building (Building 15) Course Instructor Contact Information and Office Hours210-1 Math Building (Building 15) Office hours: by appointment Course Schedule and Textbook
There is no official textbook. We list below some recommended reading containing most of the topics covered. [1] C. Houdayer, An invitation to von Neumann algebras. Available at https://cyrilhoudayer.files.wordpress.com/2014/09/vn-graduate-course.pdf [2] C. Houdayer, An introduction to II_1 factors. Available at http://perso.ens-lyon.fr/gaboriau/evenements/IHP-trimester/IHP-CIRM/Notes=Cyril=finite-vonNeumann.pdf [3] D. Kerr, H. Li, M. Pichot, Turbulence, representations, and trace-preserving actions, Proceedings of the London Mathematical Society [4] A. Kechris, Global aspects of ergodic group actions, 2010 [5] S. Popa, Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups, Inventiones Mathematicae [6] A. Furman, On Popa's cocycle superrigidity theorem, International Mathematics Research Notices [7] E. Gardella, M. Lupini, The complexity of conjugacy, orbit equivalence, and von Neumann equivalence of actions of nonamenable groups [8] A. Ioana, Orbit inequivalent actions for groups containing a copy of F_2, Inventiones Mathematicae [9] A. Ioana, Cocycle superrigidity for profinite actions of property (T) groups [10] A. Ioana, A. Kechris, T. Tsankov, Subequivalence relations and positive-definite functions [11] L. Bowen, D. Hoff, A. Ioana, von Neumann's problem and extensions of non-amenable equivalence relations [12] I. Epstein, Orbit inequivalent actions of non-amenable groups End of course projects: 1) Popa's cocycle superrigidity theorem for malleable actions. References: Theorem 5.2 in [5] and Theorem 1.3 in [6] 2) The relation of orbit equivalence of free weak mixing actions of a countable groups containing a copy of F_2 is not Borel. Theorem 2.12 of [7]; see also Section 2 of [8]. 3) Orbit equivalence superrigidity for profinite actions in the case of property (T) groups. Reference: Theorem A in [9] in the case when Gamma_0 is equal to Gamma. Course PoliciesLate work - Assignments
Midterm and Final ExamCollaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |