- the lectures are videotaped, the recordings can be found here
- for blog entries related to this class check this link
Lecture Notes
tex-version
There is now a tex-ed version of the lecture notes!
handwritten version
- Section 0: (very short) introduction into subject and history
- Section 1: The notion of freeness: definition, example, basic properties
- Section 2: The emergence of the combinatorics of FPT: free (central) limit theorem
- Section 3: The combinatorics of FPT: free cumulants
- Section 4: Free convolution of compactly supported probability measures and the R-transform
- Section 5: Free convolution of arbitrary probability measures and the subordination function
- Section 6: Gaussian random matrices and asymptotic freeness
- Section 7: Unitary random matrices and asymptotic freeness
- computer slides from the end of Section 7: Random matrices and free convolution
- Section 8: von Neumann algebras: the free group factors and relation to freeness
- Section 9: Circular and R-diagonal operators
- Section 10: Applications of freeness to vN algebras: compression of free group factors
- Section 11: Some more operator algebraic applications of free probability
