Math 209 Course Notes

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.

Suggested Presentation Topics

  • 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)

Reference Materials