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MIT OpenCourseWare

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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26 items
Last updated on May 12, 2020
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Instructor: Yufei Zhao
View the complete course: https://ocw.mit.edu/18-217F19

This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. The course also introduces students to current research topics and open problems.

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
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1. A bridge between graph theory and additive combinatorics
1:16:21
1. A bridge between graph theory and additive combinatorics

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2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem
1:12:41
2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem

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3. Forbidding a subgraph II: complete bipartite subgraph
1:16:37
3. Forbidding a subgraph II: complete bipartite subgraph

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4. Forbidding a subgraph III: algebraic constructions
1:19:45
4. Forbidding a subgraph III: algebraic constructions

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5. Forbidding a subgraph IV: dependent random choice
1:20:00
5. Forbidding a subgraph IV: dependent random choice

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6. Szemerédi's graph regularity lemma I: statement and proof
1:19:08
6. Szemerédi's graph regularity lemma I: statement and proof

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7. Szemerédi's graph regularity lemma II: triangle removal lemma
1:14:51
7. Szemerédi's graph regularity lemma II: triangle removal lemma

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8. Szemerédi's graph regularity lemma III: further applications
1:21:21
8. Szemerédi's graph regularity lemma III: further applications

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9. Szemerédi's graph regularity lemma IV: induced removal lemma
1:23:16
9. Szemerédi's graph regularity lemma IV: induced removal lemma

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10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof
1:19:14
10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof

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11. Pseudorandom graphs I: quasirandomness
1:18:20
11. Pseudorandom graphs I: quasirandomness

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12. Pseudorandom graphs II: second eigenvalue
1:19:48
12. Pseudorandom graphs II: second eigenvalue

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13. Sparse regularity and the Green-Tao theorem
1:19:06
13. Sparse regularity and the Green-Tao theorem

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14. Graph limits I: introduction
1:17:09
14. Graph limits I: introduction

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15. Graph limits II: regularity and counting
1:21:09
15. Graph limits II: regularity and counting

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16. Graph limits III: compactness and applications
1:19:52
16. Graph limits III: compactness and applications

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17. Graph limits IV: inequalities between subgraph densities
1:19:41
17. Graph limits IV: inequalities between subgraph densities

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18. Roth's theorem I: Fourier analytic proof over finite field
1:14:17
18. Roth's theorem I: Fourier analytic proof over finite field

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19. Roth's theorem II: Fourier analytic proof in the integers
1:20:09
19. Roth's theorem II: Fourier analytic proof in the integers

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20. Roth's theorem III: polynomial method and arithmetic regularity
1:20:51
20. Roth's theorem III: polynomial method and arithmetic regularity

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21. Structure of set addition I: introduction to Freiman's theorem
1:14:36
21. Structure of set addition I: introduction to Freiman's theorem

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22. Structure of set addition II: groups of bounded exponent and modeling lemma
1:19:57
22. Structure of set addition II: groups of bounded exponent and modeling lemma

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23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers
1:18:06
23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers

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24. Structure of set addition IV: proof of Freiman's theorem
1:19:31
24. Structure of set addition IV: proof of Freiman's theorem

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25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem
1:14:46
25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem

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26. Sum-product problem and incidence geometry
1:14:14
26. Sum-product problem and incidence geometry