Notes through 4/26/2017.
Change Log:

• Section 6.1.1: Dixmier's Property added
• Section 6.2: Characterizing the Commutant added

• Group measure space von Neumann algebras presented by Srivatsav Kunnawalkam Elayavalli on Monday, February 27th. Based on section 1.5 of these notes.
• Spectral theory of normal unbounded operators and applications presented by Simon Becker on Monday, Spril 3rd. Based on Chapters 5, 7, and 8 of this book.
• Morita Equivalence presented by Tim Drake on Friday, April 14th.
• Topological structure of the spectrum of a von Neumann algebra presented by Kai-chieh Chen on Friday, April 21st. Based on Chapter III.1 of this book.
• Elliptic operators, discrete groups and von Neumann algebras presented by Yingdi Qin on Monday, April 24th. Based on this paper of Atiyah.
• Ultraproducts of von Neumann algebras presented by Clark Lyons on Wednesday, April 26th.

• the functional calclulus for unbounded operators (Simon)
• $L(\Gamma)=R(\Gamma)'$ for a discrete group $\Gamma$
• Equivalent characterizations of amenability
• group-measure space construction (Srivatsav)
• topological structure of the spectrum of a von Neumann algebra (Kai-Chieh)
• Ultrapowers of von Neumann algebras
• Index of a subfactor
• Popa's deformation/rigidity: Haagerup property vs property (T)
• Construction of the interpolated free group factors
• Morita equivalence (Tim)

• Theory of Operator Algebras I by Masamichi Takesaki.
• A Course in Operator Theory by John B. Conway. Chapters 2 and 7 are especially relevant to our course. Chapter 1 offers some review of the prerequisite material.
• Von Neumann Algebras by Vaughan F.R. Jones.
• Operator Algebras: Theory of C*-Algebras and von Neumann Algebras by Bruce Blackadar. Chapter III covers many of the topics we will discuss in this course. Chapters I and II give a comprehensive overview of the prerequisite material.
• C*-algebras by Example by Kenneth R. Davidson. A standard reference for the prerequisite material.
• An Introduction to Operator Algebras by Laurent W. Marcoux. Very clearly written notes about the prerequisite material. The last chapter also covers some of the current course material.
• Notes on von Neumann algebras by Jesse Peterson. Great reference for von Neumann algebras. In particular, we will be following Sections 2.7 and 2.8.
• An Introduction to $\mathrm{II}_1$ Factors by Cyril Houdayer. Another great reference for von Neumann algebras, specifically $\mathrm{II}_1$ factors.
• Math 206 Notes by Srivatsav Kunnawalkam Elayavalli. Notes from Math 206 taught by Marc Rieffel in Fall 2016. Generously denoted by Srivatsav Kunnawalkam Elayavalli.