During the 2019 spring semester I gave a self-study course on Boolean Function Analysis.
Subjects covered:
- Basics:
- Fourier expansion.
- Orthogonality.
- Linearity testing.
- Influence.
- Fourier levels.
- Nisan–Szegedy (optional).
- Noise operator.
- Hypercontractivity:
- 4-to-2 hypercontractivity.
- Friedgut–Kalai–Naor theorem.
- Kahn–Kalai–Linial theorem.
- Friedgut’s junta theorem.
- $p$-to-$q$ hypercontractivity.
- Biased hypercube:
- $p$-biased Fourier analysis.
- Erdős–Ko–Rado theorem.
- Friedgut–Kalai sharp threshold theorem.
- Invariance principle:
- Gaussian space.
- Invariance principle.
- Majority is stablest.
Only few got to the biased hypercube, and nobody made it to the invariance principle.
Exercise sheets are available in two versions: plain, and with hints.
