Mixing of 3-term progressions in Quasirandom Groups

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Proves Gowers’ conjecture: for every finite d‑quasi‑random group the 3‑term progression counting form equals the product of expectations up to error (2/√d)^{1/4}; earlier partial results covered SL2 and finite simple groups. Proof reduces the multilinear average by repeated Cauchy‑Schwarz to a single f3 term, then uses non‑abelian Fourier and the conjugacy‑class Fourier identity (average Hilbert‑Schmidt norm² = 1/d_rho) to extract a final 1/D‑type decay.

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" chapters (14)

1. 0:00Intro
2. 0:16Expander Mixing Lemma
3. 1:59Mixing in hyper-graphs!
4. 3:45Motivations
5. 5:46Mixing in groups
6. 7:11Mixing of progressions
7. 8:38Our Result
8. 9:28Group representations
9. 10:54Irreducible representations
10. 13:08Quasirandom Groups
11. 14:30Comparison with known Results
12. 19:31Proof Comparison
13. 22:04Non-abelian Fourier
14. 27:06Conclusions and Future work