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Polynomial Methods and Incidence Theory

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

Author(s): Adam Sheffer
Series: Cambridge Studies in Advanced Mathematics 197
Publisher: Cambridge University Press
Year: 2022

Language: English
Pages: 263

Contents
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