Polynomial Methods and Incidence Theory

ISBN-13: 9781108832496 / Angielski / Twarda / 2022 / 262 str.

City University of New York Adam (Bernard M. Baruch College

Opis

A thorough yet accessible introduction to the mathematical breakthroughs achieved by using new polynomial methods in the past decade.

Spis treści

Introduction; 1. Incidences and classical discrete geometry; 2. Basic real algebraic geometry in R^2; 3. Polynomial partitioning; 4. Basic real algebraic geometry in R^d; 5. The joints problem and degree reduction; 6. Polynomial methods in finite fields; 7. The Elekes–Sharir–Guth–Katz framework; 8. Constant-degree polynomial partitioning and incidences in C^2; 9. Lines in R^3; 10. Distinct distances variants; 11. Incidences in R^d; 12. Incidence applications in R^d; 13. Incidences in spaces over finite fields; 14. Algebraic families, dimension counting, and ruled surfaces; Appendix. Preliminaries; References; Index.