| 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 |
