加性组合学Additive Combinatorics — Terence Tao & Van Vu (Cambridge Studies in Adv. Math. 105)
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第 1 章 概率方法
1.1 The first moment method — 译文+讲解 ｜ PDF
1.2 The second moment method — 译文+讲解 ｜ PDF
1.3 The exponential moment method — 译文+讲解 ｜ PDF
1.4 Correlation inequalities — 译文+讲解 ｜ PDF
1.5 The Lovász local lemma — 译文+讲解 ｜ PDF
1.6 Janson’s inequality — 译文+讲解 ｜ PDF
1.7 Concentration of polynomials — 译文+讲解 ｜ PDF
1.8 Thin bases of higher order — 译文+讲解 ｜ PDF
第 2 章 和集估计
2.2 Doubling constants — 译文+讲解 ｜ PDF
2.3 Ruzsa distance and additive energy — 译文+讲解 ｜ PDF
2.4 Covering lemmas — 译文+讲解 ｜ PDF
2.5 The Balog–Szemerédi–Gowers theorem — 译文+讲解 ｜ PDF
2.6 Symmetry sets and imbalanced partial sum sets — 译文+讲解 ｜ PDF
第 3 章 加性几何
3.1 Additive groups — 译文+讲解 ｜ PDF
3.2 Progressions — 译文+讲解 ｜ PDF
3.3 Convex bodies — 译文+讲解 ｜ PDF
3.4 The Brunn–Minkowski inequality — 译文+讲解 ｜ PDF
第 4 章 傅里叶分析方法
4.1 Basic theory — 译文+讲解 ｜ PDF
4.5 Lambda( p) constants, Bh[g] sets, and dissociated sets — 译文+讲解 ｜ PDF
第 5 章 逆和集定理
5.1 Minimal size of sum sets and the e-transform — 译文+讲解 ｜ PDF
5.2 Sum sets in vector spaces — 译文+讲解 ｜ PDF
5.3 Freiman homomorphisms — 译文+讲解 ｜ PDF
5.4 Torsion and torsion-free inverse theorems — 译文+讲解 ｜ PDF
第 6 章 图论方法
6.1 Basic Notions — 译文+讲解 ｜ PDF
6.2 Independent sets, sum-free subsets, and Sidon sets — 译文+讲解 ｜ PDF
6.3 Ramsey theory — 译文+讲解 ｜ PDF
6.4 Proof of the Balog–Szemerédi–Gowers theorem — 译文+讲解 ｜ PDF
第 7 章 Littlewood–Offord 问题
7.1 The combinatorial approach — 译文+讲解 ｜ PDF
7.2 The Fourier-analytic approach — 译文+讲解 ｜ PDF
7.3 The Esséen concentration inequality — 译文+讲解 ｜ PDF
7.4 Inverse Littlewood–Offord results — 译文+讲解 ｜ PDF
第 8 章 关联几何
8.1 The crossing number of a graph — 译文+讲解 ｜ PDF
8.2 The Szemerédi–Trotter theorem — 译文+讲解 ｜ PDF
8.3 The sum-product problem in R — 译文+讲解 ｜ PDF
8.4 Cell decompositions and the distinct distances problem — 译文+讲解 ｜ PDF
第 9 章 代数方法
9.1 The combinatorial Nullstellensatz — 译文+讲解 ｜ PDF
9.2 Restricted sum sets — 译文+讲解 ｜ PDF
9.3 Snevily’s conjecture — 译文+讲解 ｜ PDF
9.4 Finite fields — 译文+讲解 ｜ PDF
9.5 Davenport’s problem — 译文+讲解 ｜ PDF
9.6 Kemnitz’s conjecture — 译文+讲解 ｜ PDF
9.7 Stepanov’s method — 译文+讲解 ｜ PDF
9.8 Cyclotomic fields, and the uncertainty principle — 译文+讲解 ｜ PDF
第 10 章 k=3 的 Szemerédi 定理
10.1 General strategy — 译文+讲解 ｜ PDF
10.2 The small torsion case — 译文+讲解 ｜ PDF
10.3 The integer case — 译文+讲解 ｜ PDF
10.4 Quantitative bounds — 译文+讲解 ｜ PDF
10.5 An ergodic argument — 译文+讲解 ｜ PDF
第 11 章 k>3 的 Szemerédi 定理
11.1 Gowers uniformity norms — 译文+讲解 ｜ PDF
11.2 Hard obstructions to uniformity — 译文+讲解 ｜ PDF
11.3 Proof of Theorem 11.6 — 译文+讲解 ｜ PDF
11.4 Soft obstructions to uniformity — 译文+讲解 ｜ PDF
11.5 The infinitary ergodic approach — 译文+讲解 ｜ PDF