Applications in Extremal Combinatorics 1

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Survey of how junta-style decompositions and Fourier-type bases give concrete extremal bounds: Friedgut and Kindler–Safra analogues extend to families, S_n and GL_q, and yield q‑norm/character bounds for large conjugacy classes; the p‑biased Erdős–Ko–Rado bound is proved by a p‑biased noise operator diagonalized by a new orthonormal basis, with a coupling allowing negative ε up to -p/(1-p); failure of a naive level inequality motivates hypercontractivity for global functions, which recovers exponential improvements in the intersecting‑family estimates.

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" chapters (10)

1. 0:00Junta method in extremal combinatorics
2. 2:06Juntas in Boolean functions
3. 8:05Juntas in set systems
4. 16:42Juntas in GL_q and representation
5. 26:00Juntas in character theory
6. 30:01Motivation for extremal combinatorics
7. 36:23Erdos-Ko-Rado theorem
8. 42:00Noise operator and Fourier basis
9. 58:39Global functions and level inequality
10. 1:00:44Q&A