Prerequisites:
Basic operator algebra theory (such as the material
of Peterson's introduction to operator algebras, spring 09). Work
through Kehe Zhu's An Introduction to Operator Algebras,
CRC Press, 1993, if you have not taken Peterson's course.
Recommended Books: Some of the material covered in the course
can be found in the following books:
1) Jacques Dixmier, Von Neumann Algebras, North Holland, 1981.
2) Vaughan Jones, V. Sunder, Introduction to Subfactors,
Cambridge University Press, 1997.
3) Masamichi Takesaki, Theory of Operator Algebras I, II, III,
Springer-Verlag 2002.
4) David Evans, Y. Kawahigashi, Quantum Symmetries on Operator
Algebras, Oxford University Press, 1998.
5) Serban Stratila, Laszlo Zsido, Lectures on Von Neumann Algebras.
Additional references will be given throughout the course.
Syllabus: The contents of the course will depend on the
background of the audience. As of now, I plan to start the course
with some of the basics of the theory of von Neumann algebras,
such as the group measure space
construction, group von Neumann algebras, bimodules, Connes' bimodule
tensor product and the Murray-von Neumann coupling constant.
I will then discuss Jones' theory of subfactors and will try to get
as quickly as possible to the forefront of research in
subfactors and planar algebras. I plan to include a discussion of
how Jones' braid group representation and
his knot invariant, the Jones polynomial, arise naturally from subfactor
theory.
Grading:
The course grade will be based on attendance and possibly a
presentation. I will give out optional homework problems. There will be no
exams.