Preface
Acknowledgments
Chapter 1. Higher order Fourier analysis
1.1. Equidistribution of polynomial sequences in tori
1.2. Roth's theorem
1.3. Linear patterns
1.4. Equidistribution of polynomials over finite fields
1.5. The inverse conjecture for the Gowers norm I. The finite field case
1.6. The inverse conjecture for the Gowers norm II. The integer case
1.7. Linear equations in primes
Chapter 2. Related articles
2.1. Ultralimit analysis and quantitative algebraic geometry
2.2. Higher order Hilbert spaces
2.3. The uncertainty principle
Bibliography
Index
