SEARCH COURSES

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

(26 Lectures Available)


S# 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 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
3 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
4 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
5 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
6 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
7 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
8 8. Szemerédi's graph regularity lemma III: further applications (M-I-T) Graph Theory and Additive Combinatorics, Fall 2019 (M-I-T) MIT Prof. Yufei Zhao Basic and Health Sciences
9 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
10 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
11 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
12 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
13 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
14 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
15 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
16 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
17 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
18 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
19 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
20 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
21 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
22 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
23 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
24 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
25 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

of 2 26 Lectures Available.