Calendar

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

Course Info

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assignment Problem Sets
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