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  3. Polynomial Methods and Incidence Theory
  • Cited by 8
  • Adam Sheffer, Bernard M. Baruch College, City University of New York
Publisher:
Cambridge University Press
Online publication date:
March 2022
Print publication year:
2022
Online ISBN:
9781108959988
DOI:
https://doi.org/10.1017/9781108959988
Subjects:
Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Discrete Mathematics Information Theory and Coding
Series:
Cambridge Studies in Advanced Mathematics (197)
Information

Book description

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.

Reviews

‘This book gives a very nice introduction to the areas of incidence geometry and the polynomial method … Since this area of mathematics is still rather young, the book contains many open problems - this helps to bring the reader to the front of research. Furthermore, each chapter is followed by a generous amount of exercises.’

Audie Warren Source: zbMATH Open

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