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Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
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Lecture
Course
Institute
Instructor
Discipline
1
1. A bridge between graph theory and additive combinatorics (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
2
10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
3
11. Pseudorandom graphs I: quasirandomness (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
4
12. Pseudorandom graphs II: second eigenvalue (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
5
13. Sparse regularity and the Gree-Tao theorem (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
6
14. Graph limits I: introduction (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
7
15. Graph limits II: regularity and counting (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
8
16. Graph limits III: compactness and applications (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
9
17. Graph limits IV: inequalities between subgraph densities (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
10
18. Roth's theorem I: Fourier analytic proof over finite field (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
11
19. Roth's theorem II: Fourier analytic proof in the integers (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
12
2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
13
20. Roth's theorem III: polynomial method and arithmetic regularity (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
14
21. Structure of set addition I: introduction to Freiman's theorem (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
15
22. Structure of set addition II: groups of bounded exponent and modeling lemma (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
16
9. Szemerédi's graph regularity lemma IV: induced removal lemma (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
17
23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
18
24. Structure of set addition IV: proof of Freiman's theorem (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
19
25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
20
26. Sum-product problem and incidence geometry (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
21
3. Forbidding a subgraph II: complete bipartite subgraph (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
22
4. Forbidding a subgraph III: algebraic constructions (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
23
5. Forbidding a subgraph IV: dependent random choice (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
24
6. Szemerédi's graph regularity lemma I: statement and proof (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
25
7. Szemerédi's graph regularity lemma II: triangle removal lemma (M-I-T)
Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T)
MIT
Prof. Yufei Zhao
Basic and Health Sciences
1
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