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Polynomial methods and incidence theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Polynomial methods and incidence theoryAdam Sheffer.
Author:	Sheffer, Adam.
Published:	Cambridge :Cambridge University Press,2022.
Description:	xvi, 245 p. :ill., digital ;23 cm.
Notes:	Title from publisher's bibliographic system (viewed on 18 Mar 2022).
Subject:	Combinatorial geometry.
Online resource:	https://doi.org/10.1017/9781108959988
ISBN:	9781108959988$q(electronic bk.)

Polynomial methods and incidence theory
Sheffer, Adam.

Polynomial methods and incidence theory[electronic resource] /Adam Sheffer. - Cambridge :Cambridge University Press,2022. - xvi, 245 p. :ill., digital ;23 cm. - Cambridge studies in advanced mathematics ;197. - Cambridge studies in advanced mathematics ;105..

Title from publisher's bibliographic system (viewed on 18 Mar 2022).

The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.

ISBN: 9781108959988$q(electronic bk.)Subjects--Topical Terms:

190923
Combinatorial geometry.

LC Class. No.: QA167 / .S357 2022

Dewey Class. No.: 511.66

Polynomial methods and incidence theory
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245 1 0 $a Polynomial methods and incidence theory $h [electronic resource] / $c Adam Sheffer.
260 $a Cambridge : $b Cambridge University Press, $c 2022.
300 $a xvi, 245 p. : $b ill., digital ; $c 23 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 197
500 $a Title from publisher's bibliographic system (viewed on 18 Mar 2022).
520 $a The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. There has also been significant progress on a variety of problems from additive combinatorics, discrete geometry, and more. This book gives a detailed yet accessible introduction to these new polynomial methods and their applications, with a focus on incidence theory. Based on the author's own teaching experience, the text requires a minimal background, allowing graduate and advanced undergraduate students to get to grips with an active and exciting research front. The techniques are presented gradually and in detail, with many examples, warm-up proofs, and exercises included. An appendix provides a quick reminder of basic results and ideas.
650 0 $a Combinatorial geometry. $3 190923
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Discrete geometry. $3 277229
650 0 $a Finite fields (Algebra) $3 359950
650 0 $a Partitions (Mathematics) $3 239773
650 0 $a Incidence algebras. $3 487284
650 0 $a Polynomials. $3 184760
830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 541725
856 4 0 $u https://doi.org/10.1017/9781108959988