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.

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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.