• the lectures are videotaped, the recordings can be found on this youtube playlist
• for blog entries related to this class check this link
• the homepage of the course can be found here

Lecture Notes

pdf-version

Finally, there is now also a pdf-version of the

Non-commutative Distributions Lecture Notes

handwritten version

Section 0: Introduction

• see Lecture 1 (first half)

Section 1: Basic Definitions and Examples

• see Lecture 1 (second half) and Lecture 2

Section 2: Operator-Valued Distribution and Operator-Valued Cauchy Transform

• see Lecture 3

 Section 3: Non-Commutative Functions: Motivations and Formal Aspects

• see Lecture 4, Lecture 5 and Lecture 6 (first half)

Section 4: The Operator-Valued Cauchy Transform

• see Lecture 6 (second half), Lecture 7 and Lecture 8

Section 5: Operator-Valued Freeness

• see Lecture 9, Lecture 10, Lecture 11 and Lecture 12 (first part)

Section 6 (part 1, part 2): Operator-Valued Central Limit Theorem and Operator-Valued Semicircular Elements

• see Lecture 12 (second half), Lecture 13, Lecture 14 and Lecture 15 (beginning)

Section 7: Matrices of Semicirculars and Matrix-Valued Semicirculars (and Block Random Matrices)

• see Lecture 15

Section 8: Polynomials in Free Semicirculars and Linearization

• see Lecture 16 and Lecture 17 (beginning)

Section 9: Combinatorial and Analytic Description of Operator-Valued Freeness: Free Cumulants and R-Transform

• see Lecture 17 (second half) and Lecture 18 (first half)

Section10: Operator-Valued Free Convolution via Subordination Function and the Distribution of Polynomials in Free Variables

• see Lecture 18 (second half)

Computer slides from the end of Section 10 (beginning of Lecture 19)

Section 11: Distribution of Rational Expressions in Free Random Variables

• see Lecture 19

Section 12: Unbounded Rational Expressions

• see Lecture 20
• my talk at the Fields Institute covers also similar topics