Graph Theory and Additive Combinatorics

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