Fall Semester 2005, II1 Factors and Subfactors
(Math 390A)



Instructor: Dietmar Bisch
Lecture: TuTh, 9:35am-10:50am, SC 1403
Office: SC 1405, (615) 322-1999 or SC 1334, (615) 322-4168 (Chair's office)
Office hours: TuTh 10:50am-11:30am
Mailbox: SC 1326


Special schedule note: We have 3 special class meetings on 8/22, 8/23 and 8/24 from 11am to 12:15pm in SC 1403. The regular class meetings on 8/25, 8/30 and 9/1 are cancelled.


Prerequisites: A course on von Neumann algebras.

Recommended Books: The following books contain some of the background material for what I plan to cover in the course:
1) Jacques Dixmier, Von Neumann Algebras, North Holland, 1981.
2) Kehe Zhu, An Introduction to Operator Algebras, CRC Press, 1993.
3) Vaughan Jones, V. Sunder, Introduction to Subfactors, Cambridge University Press, 1997.
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) Richard Kadison, John Ringrose, Fundamentals of the Theory of Operator Algebras, I, II, III, IV, AMS, 1997, 1997, 1991, 1992.
8) Serban Stratila, Laszlo Zsido, Lectures on Von Neumann Algebras.

Additional references will be given throughout the course.

Syllabus: This course is a continuation of Introduction to von Neumann algebras which I taught in spring 2005. I will continue the discussion of the coupling constant and then discuss the Jones index for subfactors. I will prove Jones' rigidity theorem and present Jones' braid group representation and his knot invariant, the Jones polynomial. I will then move on to some special topics from the theory of subfactors, for instance planar algebras. Other possible topics are applications of rigidity phenomena (property (T)) and L2-Betti numbers to the structure theory of II1 factors, including recent solutions to some longstanding problems in the theory of II1 factors due to Popa.

Grading: The course grade will be based on attendance and a presentation. I will give out optional homework problems. There will be no exams.