Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)

• 1. A bridge between graph theory and additive combinatorics (M-I-T)
• 2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem (M-I-T)
• 3. Forbidding a subgraph II: complete bipartite subgraph (M-I-T)
• 4. Forbidding a subgraph III: algebraic constructions (M-I-T)
• 5. Forbidding a subgraph IV: dependent random choice (M-I-T)
• 6. Szemerédi's graph regularity lemma I: statement and proof (M-I-T)
• 7. Szemerédi's graph regularity lemma II: triangle removal lemma (M-I-T)
• 8. Szemerédi's graph regularity lemma III: further applications (M-I-T)
• 9. Szemerédi's graph regularity lemma IV: induced removal lemma (M-I-T)
• 10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof (M-I-T)
• 11. Pseudorandom graphs I: quasirandomness (M-I-T)
• 12. Pseudorandom graphs II: second eigenvalue (M-I-T)
• 13. Sparse regularity and the Gree-Tao theorem (M-I-T)
• 14. Graph limits I: introduction (M-I-T)
• 15. Graph limits II: regularity and counting (M-I-T)
• 16. Graph limits III: compactness and applications (M-I-T)
• 17. Graph limits IV: inequalities between subgraph densities (M-I-T)
• 18. Roth's theorem I: Fourier analytic proof over finite field (M-I-T)
• 19. Roth's theorem II: Fourier analytic proof in the integers (M-I-T)
• 20. Roth's theorem III: polynomial method and arithmetic regularity (M-I-T)
• 21. Structure of set addition I: introduction to Freiman's theorem (M-I-T)
• 23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers (M-I-T)
• 24. Structure of set addition IV: proof of Freiman's theorem (M-I-T)
• 25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem (M-I-T)
• 26. Sum-product problem and incidence geometry (M-I-T)