1 
1. A bridge between graph theory and additive combinatorics (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

2 
2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

3 
3. Forbidding a subgraph II: complete bipartite subgraph (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

4 
4. Forbidding a subgraph III: algebraic constructions (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

5 
5. Forbidding a subgraph IV: dependent random choice (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

6 
6. Szemerédi's graph regularity lemma I: statement and proof (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

7 
7. Szemerédi's graph regularity lemma II: triangle removal lemma (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

8 
8. Szemerédi's graph regularity lemma III: further applications (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

9 
9. Szemerédi's graph regularity lemma IV: induced removal lemma (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

10 
10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

11 
11. Pseudorandom graphs I: quasirandomness (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

12 
12. Pseudorandom graphs II: second eigenvalue (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

13 
13. Sparse regularity and the GreeTao theorem (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

14 
14. Graph limits I: introduction (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

15 
15. Graph limits II: regularity and counting (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

16 
16. Graph limits III: compactness and applications (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

17 
17. Graph limits IV: inequalities between subgraph densities (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

18 
18. Roth's theorem I: Fourier analytic proof over finite field (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

19 
19. Roth's theorem II: Fourier analytic proof in the integers (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

20 
20. Roth's theorem III: polynomial method and arithmetic regularity (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

21 
21. Structure of set addition I: introduction to Freiman's theorem (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

22 
22. Structure of set addition II: groups of bounded exponent and modeling lemma (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

23 
23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

24 
24. Structure of set addition IV: proof of Freiman's theorem (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences

25 
25. Structure of set addition V: additive energy and BalogSzemerédiGowers theorem (MIT)

Graph Theory and Additive Combinatorics, Fall 2019 (MIT)

MIT

Prof. Yufei Zhao

Basic and Health Sciences
