TY  - BOOK
AU  - Guth,Larry
TI  - Polynomial methods in combinatorics
T2  - University lecture series
SN  - 9781470428907 (pbk. : acidfree paper)
U1  - 511.66 23
PY  - 2016///
CY  - Providence : 
PB  - American Mathematical Society, 
KW  - Combinatorial geometry
KW  - Polynomials
KW  - Algebraic geometry
N1  - 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
N2  - 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
ER  -