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1. A bridge between graph theory and additive combinatorics (M-I-T)
Course:
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
Discipline:
Basic and Health Sciences
Institute:
MIT
Instructor(s):
Prof. Yufei Zhao
Level:
Graduate
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
1. A bridge between graph theory and additive combinatorics (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)
2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem (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)
22. Structure of set addition II: groups of bounded exponent and modeling lemma (M-I-T)
9. Szemerédi's graph regularity lemma IV: induced removal lemma (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)
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)
