Higher-Order Fourier Analysis and Applications

ISBN-13: 9781680835922 / Angielski / Miękka / 2019 / 230 str.

Hamed Hatami; Shachar Lovett; Pooya Hatami

Spis treści

• 1. Introduction
• Part I. Low Degree Testing
• 2. Low Degree Testing
• 3. Low-degree Tests, the 99% Regime
• 4. Low-degree Tests, the 1% Regime
• 5. Gowers Norms, the Inverse Gowers Conjecture and its Failure
• Part II. Higher Order Fourier Analysis
• 6. Nonclassical Polynomials, and the Inverse Gowers Theorem
• 7. Rank, Regularity, and Other Notions of Uniformity
• 8. Bias vs Low Rank in Large Fields
• 9. Decomposition Theorems
• 10. Homogeneous Nonclassical Polynomials
• 11. Complexity of Systems of Linear Forms
• 12. Deferred Technical Proofs
• 13. Algorithmic Regularity
• Part III. Algebraic Property Testing
• 14. Algebraic Properties
• 15. One-Sided Algebraic Property Testing
• 16. Degree Structural Properties
• 17. Estimating the Distance from Algebraic Properties
• Part IV. Open Problems
• 18. Open Problems
• References