LEC # | TOPICS | KEY DATES |
---|---|---|

1 | A bridge between graph theory and additive combinatorics | |

Part I: Graph theory |
||

2 | Forbidding a subgraph I: Mantel’s theorem and Turán’s theorem | |

3 | Forbidding a subgraph II: Complete bipartite subgraph | |

4 | Forbidding a subgraph III: Algebraic constructions | |

5 | Forbidding a subgraph IV: Dependent random choice | |

6 | Szemerédi’s graph regularity lemma I: Statement and proof | Problem set 1 due |

7 | Szemerédi’s graph regularity lemma II: Triangle removal lemma | |

8 | Szemerédi’s graph regularity lemma III: Further applications | |

9 | Szemerédi’s graph regularity lemma IV: Induced removal lemma | |

10 | Szemerédi’s graph regularity lemma V: Hypergraph removal and spectral proof | Problem set 2 due |

11 | Pseudorandom graphs I: Quasirandomness | |

12 | Pseudorandom graphs II: Second eigenvalue | |

13 | Sparse regularity and the Green-Tao theorem | Problem set 3 due |

14 | Graph limits I: Introduction | |

15 | Graph limits II: Regularity and counting | |

16 | Graph limits III: Compactness and applications | |

17 | Graph limits IV: Inequalities between subgraph densities | Problem set 4 due |

Part II: Additive combinatorics |
||

18 | Roth’s theorem I: Fourier analytic proof over finite field | |

19 | Roth’s theorem II: Fourier analytic proof in the integers | |

20 | Roth’s theorem III: Polynomial method and arithmetic regularity | Problem set 5 due |

21 | Structure of set addition I: Introduction to Freiman’s theorem | |

22 | Structure of set addition II: Groups of bounded exponent and modeling lemma | |

23 | Structure of set addition III: Bogolyubov’s lemma and the geometry of numbers | |

24 | Structure of set addition IV: Proof of Freiman’s theorem | |

25 | Structure of set addition V: Additive energy and Balog-Szemerédi-Gowers theorem | |

26 | Sum-product problem and incidence geometry | Problem set 6 due |