Coverart for item
The Resource Polynomial methods and incidence theory, Adam Sheffer, (electronic resource)

Polynomial methods and incidence theory, Adam Sheffer, (electronic resource)

Label
Polynomial methods and incidence theory
Title
Polynomial methods and incidence theory
Statement of responsibility
Adam Sheffer
Creator
Subject
Language
eng
Summary
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös'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"--
Assigning source
Provided by publisher
Cataloging source
LBSOR/DLC
http://library.link/vocab/creatorName
Sheffer, Adam
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Cambridge studies in advanced mathematics
Series volume
197
http://library.link/vocab/subjectName
  • Combinatorial geometry
  • Polynomials
  • Incidence algebras
  • Partitions (Mathematics)
  • Finite fields (Algebra)
  • Discrete geometry
  • Geometry, Algebraic
Label
Polynomial methods and incidence theory, Adam Sheffer, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
Incidences and classical discrete geometry -- Basic real algebraic geometry in R2 -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Constant-degree polynomial partitioning and incidences in C2 -- Lines in R3 -- Distinct distances variants -- Incidences in Rd -- Incidence applications in Rd -- Incidences in spaces over finite field -- Algebraic families, dimension counting, and ruled surfaces
Control code
ssj0002574588
Dimensions
unknown
Extent
1 online resource (pages cm.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9781108832496
Lccn
2021063054
Specific material designation
remote
System control number
(WaSeSS)ssj0002574588
Label
Polynomial methods and incidence theory, Adam Sheffer, (electronic resource)
Publication
Bibliography note
Includes bibliographical references and index
Contents
Incidences and classical discrete geometry -- Basic real algebraic geometry in R2 -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Constant-degree polynomial partitioning and incidences in C2 -- Lines in R3 -- Distinct distances variants -- Incidences in Rd -- Incidence applications in Rd -- Incidences in spaces over finite field -- Algebraic families, dimension counting, and ruled surfaces
Control code
ssj0002574588
Dimensions
unknown
Extent
1 online resource (pages cm.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9781108832496
Lccn
2021063054
Specific material designation
remote
System control number
(WaSeSS)ssj0002574588

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