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  3. Polynomial Methods and Incidence Theory
  • Cited by 8
      • Adam Sheffer, Bernard M. Baruch College, City University of New York
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2022
      March 2022
      ISBN:
      9781108959988
      9781108832496
      DOI:
      https://doi.org/10.1017/9781108959988
      Dimensions:
      (235 x 157 mm)
      Weight & Pages:
      0.54kg, 262 Pages
      Dimensions:
      Weight & Pages:
      • 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)
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    • Selected: Digital
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    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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