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Polynomial methods in combinatorics / Larry Guth.

By: Material type: TextTextSeries: University lecture series ; v 64.Publication details: Providence : American Mathematical Society, ©2016.Description: ix, 273 pages : illustrations ; 26 cmISBN:
  • 9781470428907 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 511.66 23 G984
Contents:
1. Introduction -- 2. Fundamental examples of the polynomial method -- 3. Why polynomials? -- 4. The polynomial method in error-correcting codes -- 5. On polynomials and linear algebra in combinatorics -- 6. The Bezout theorem -- 7. Incidence geometry -- 8. Incidence geometry in three dimensions -- 9. Partial symmetries -- 10. Polynomial partitioning -- 11. Combinatorial structure, algebraic structure, and geometric structure -- 12. An incidence bound for lines in three dimensions -- 13. Ruled surfaces and projection theory -- 14. The polynomial method in differential geometry -- 15. Harmonic analysis and the Kakeya problem -- 16. The polynomial method in number theory -- Bibliography.
Summary: Explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields. The author also discusses in detail various problems in incidence geometry associated to Paul Erdos's distinct distances problem in the plane from the 1940s.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.66 G984 (Browse shelf(Opens below)) Available 138109
Total holds: 0

Includes bibliographical references.

1. Introduction --
2. Fundamental examples of the polynomial method --
3. Why polynomials? --
4. The polynomial method in error-correcting codes --
5. On polynomials and linear algebra in combinatorics --
6. The Bezout theorem --
7. Incidence geometry --
8. Incidence geometry in three dimensions --
9. Partial symmetries --
10. Polynomial partitioning --
11. Combinatorial structure, algebraic structure, and geometric structure --
12. An incidence bound for lines in three dimensions --
13. Ruled surfaces and projection theory --
14. The polynomial method in differential geometry --
15. Harmonic analysis and the Kakeya problem --
16. The polynomial method in number theory --
Bibliography.

Explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields. The author also discusses in detail various problems in incidence geometry associated to Paul Erdos's distinct distances problem in the plane from the 1940s.

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