Applications in Extremal Combinatorics 2

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Shows hypercontractivity for global functions combined with a decomposition into global parts to convert level‑d inequalities into exponentially stronger Erdos–Ko–Rado–type bounds; uses junta reduction, a coupling that transfers hypercontractivity from the uniform cube to p‑bias, and representation‑theoretic eigenvalue estimates (trace/Hoffman method) on Sn. Proves the Erdos intersection cases for most k (k up to about (1/2−ε)n) and settles the product‑free extremal problem in An for large n, after prior bounds n^{-3} (Gowers) and ~n^{-1/2} (Eberhard). Ends with exact extremal structure in An.

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" chapters (11)

1. 0:00Extremal combinatorics
2. 2:51Intersection problems
3. 7:36Junta methods
4. 12:36Structure of families
5. 17:27Hypercontractivity
6. 21:26Product-free sets in groups
7. 25:07The alternating group
8. 30:12Spectral methods
9. 35:33Representation theory
10. 41:16Global functions
11. 50:16Coupling approach