Date |
Material covered |
Reference |
Video |
January 25 |
Introduction/Invariant measure and Vitali sets
|
|
Lecture 1
|
January 27 |
Banach Tarski Paradox/Amenable groups, paradoxical decomposition
|
2.6 in [BO]
|
Lecture 2 |
January 29 |
Amenable groups II/Folner sequences, almost invariant vectors.
|
2.6 in [BO]
|
Lecture 3 |
February 1 |
Operator algebras associated to amenable groups, Relative property (T)
|
12.1 in [BO]
|
Lecture 4 |
February 3 |
Relative property (T) for (Z^2, SL(2, Z) \ltimes Z^2)
|
12.1 in [BO]
|
Lecture 5 |
February 5 |
Positive definite functions/cocycles and Schoenberg's theorem
|
Appendix D in [BO]
|
Lecture 6 |
February 8 |
Characterizations of relative property (T)
|
12.1 in [BO]
|
Lecture 7 |
February 10 |
Property (T) and reduced cohomology
|
12.1 in [BO]
|
Lecture 8 |
February 12 |
Property (T) for SL(3, Z)
|
12.1 in [BO]
|
Lecture 9 |
February 15 |
Haagerup's property for free groups
|
12.2 in [BO]
|
Lecture 10 |
February 17 |
Haagerup's property and wreath products
|
12.2 in [BO]
|
Lecture 11 |
February 19 |
Finite von Neumann algebras
|
Review of selected sections in [AP]
|
Lecture 12 |
February 22 |
Completely positive maps/Correspondences
|
13.1 in [AP]
|
Lecture 13 |
February 24 |
Applications to II_1 factors
|
14.4 in [AP]
|
Lecture 14 |
February 26 |
Property (Gamma) and inner-amenability
|
15.4 in [AP]
|
|
February 26 |
Hyperbolic graphs/groups
|
5.3 in [BO]
|
|
February 26 |
Hyperbolic graphs/groups II
|
5.3 in [BO]
|
|
February 26 |
Amenable actions
|
4.3 in [BO]
|
|
February 26 |
Exact groups
|
5.1 in [BO]
|
|
March 1 |
Biexact groups
|
15.2 in [BO]
|
|
March 3 |
Wreath products and Haagerup's property
|
12.2 in [BO]
|
|
March 5 |
Wreath products and biexactness
|
15.3 in [BO]
|
|
March 8 |
Acylindrically hyperbolic groups
|
[Os]
|
|
March 10 |
Acylindrical actions on Quasi-trees
|
[Ba]
|
|
March 12 |
Quasi-cocycles from quasi-trees
|
[BFF]
|
|
March 15 |
Herz-Schur multipliers
|
Appendix D in [BO]
|
|
March 17 |
Herz-Schur multipliers II
|
Appendix D in [BO]
|
|
March 19 |
Weak amenability
|
12.3 in [BO]
|
|
March 22 |
Weak amenability for free groups
|
12.3 in [BO]
|
|
March 24 |
Weak amenability for hyperbolic groups
|
[Oz]
|
|
March 26 |
Non-weak amenability for wreath products
|
12.3 in [BO]
|
|
March 29 |
Operator systems and completely positive maps
|
Chapter 3 in [P]
|
|
March 31 |
Arveson's Extension Theorem
|
Chapter 7 in [P]
|
|
April 5 |
Operator spaces and completely bounded maps
|
Chapter 8 in [P]
|
|
April 7 |
Wittstock's Extension Theorem
|
Chapter 8 in [P]
|
|
April 9 |
The Haagerup tensor product
|
Chapter 17 in [P]
|
|
April 12 |
Completely bounded multilinear maps
|
Chapter 17 in [P]
|
|
April 14 |
Multivariable Herz-Schur multipliers
|
[ER]
|
|
April 16 |
Multivariable Herz-Schur multipliers II
|
[ER]
|
|
April 19 |
Applications to von Neumann algebras I
|
|
|
April 21 |
Applications to von Neumann algebras II
|
|
|
April 23 |
|
|
|
April 26 |
|
|
|
April 28 |
|
|
|
April 28 |
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