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Brent Nelson
UC Berkeley Department of Mathematics
Research
Teaching
Conferences
Curriculum Vitae
About Me
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
Presentations
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
(
Γ
)
=
R
(
Γ
)
′
for a discrete group
Γ
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
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
I
I
1
Factors
by Cyril Houdayer.
Another great reference for von Neumann algebras, specifically
I
I
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.
Announcements:
There will be two additional (optional) lectures during RRR week on Monday, May 1st and Wednesday, May 3rd in the usual time/place.
Course Materials:
Course Syllabus
Office Hours (Evans 851):
Wednesdays 3:30 pm - 5:30 pm
Fridays 1:00 pm - 2:00 pm