Prerequisites: Basic operator algebra theory such as MATH 8120 or Kehe Zhu's An Introduction to Operator Algebras, CRC Press, 1993.

Suggested Books: There will be no textbook. Some of the material covered in the course can be found in the following books:
1) Serban Stratila, Laszlo Zsido, Lectures on Von Neumann Algebras.
2) Vaughan Jones, V. Sunder, Introduction to Subfactors, Cambridge University Press, 1997.
3) Jacques Dixmier, Von Neumann Algebras, North Holland, 1981.
4) Masamichi Takesaki, Theory of Operator Algebras I, II, III, Springer-Verlag 2002.
5) David Evans, Y. Kawahigashi, Quantum Symmetries on Operator Algebras, Oxford University Press, 1998.
6) Fred Goodman, Pierre de la Harpe, Vaughan Jones, Coxeter Graphs and Towers of Algebras, Springer 1989, reprint 2011.

Additional references will be given throughout the course.

Syllabus: The course will cover topics in von Neumann algebras beyond an introductory course in operator algebras (such as MATH 8120). I will introduce and discuss the types of von Neumann algebras, factors, normal functionals and representations, bimodules and the Murray-von Neumann coupling constant. Throughout this part of the course, I will present topics from the theory of II₁ factors, including group measure space construction and group von Neumann algebras. I will then move on to Jones' theory of subfactors and cover basic properties of the Jones index, the basic construction and present invariants and constructions for subfactors. If time allows, I plan to include a discussion of Jones' braid group representation that arises from subfactors, and his knot invariant, the Jones polynomial.

The precise contents of the course will depend on the background and interests of the audience.

Grading: The course grade will be based on attendance and a (team) presentation. I will assign optional homework problems. There will be no exams.

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