Adam Sheffer (City University of New Yor Bernard M. Baruch College

Polynomial Methods and Incidence Theory

• Gebundenes Buch

Produktbeschreibung

This is a detailed introduction to the new polynomial methods responsible for numerous major mathematical breakthroughs in the past decade. It requires a minimal background and includes many examples, warm-up proofs, and exercises, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front.

Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• Seitenzahl: 262
• Erscheinungstermin: 10. März 2022
• Englisch
• Abmessung: 235mm x 157mm x 20mm
• Gewicht: 542g
• ISBN-13: 9781108832496
• ISBN-10: 1108832490
• Artikelnr.: 63201216

Autorenporträt

Adam Sheffer is Mathematics Professor at CUNY's Baruch College and the CUNY Graduate Center. Previously, he was a postdoctoral researcher at the California Institute of Technology. Sheffer's research work is focused on polynomial methods, discrete geometry, and additive combinatorics.

Inhaltsangabe

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.