Topics in Combinatorics: Analysis of Boolean Functions

Lecture Notes

Lecture 1: Course Overview and the Basic Set-Up (PDF)

Lecture 2: The BLR Linearity Test and Random Restrictions (PDF)

Lecture 3: PAC Learning and Learning Sparse Functions (PDF)

Lecture 4: Influences of Boolean Functions (PDF)

Lecture 5: Hypercontractive Inequality (PDF)

Lecture 6: The FKN Theorem and the KKL Theorem (PDF)

Lecture 7: Talagrand’s Version of the KKL Theorem, the Friedgut Junta Theorem, and Isoperimetric Inequalities (PDF)

Lectures 8–10: Noise Stability and Arrow’s Impossibility Theorem (PDF) 

Lectures 11–12: Erdos-Ko-Rado Type Theorem, the p-biased Cube, and Properties of Quasi-random Families (PDF)

Lectures 13–14: Invariance Principle, the Berry-Essen Theorem, and Hypercontractivity in Gaussian Space (PDF)

Lecture 15: Introduction to Complexity Theory, Approximation Problems, and the PCP Theorem (PDF)

Lecture 16: The Goemans-Williamson Algorithm and A Hardness Result for Max-Cut (PDF)

Lecture 17: Preliminaries, the Reduction, and Analysis of the Reduction (PDF)