• 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