Polynomial Methods and Incidence Theory

Adam Sheffer

2022年3月 · Cambridge Studies in Advanced Mathematics 197 巻 · Cambridge University Press

電子書籍

264

ページ

評価とレビューは確認済みではありません詳細

この電子書籍について

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.

著者について

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.