Book Review
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Book Information:
Author:
Larry Guth
Title:
Polynomial methods in combinatorics
Additional book information:
University Lecture Series, Vol. 64,
American Mathematical Society,
Providence, RI,
2016,
ix+273 pp.,
ISBN 978-1-4704-2890-7,
US $48.00,
softcover
Zeev Dvir, On the size of Kakeya sets in finite fields, J. Amer. Math. Soc. 22 (2009), no. 4, 1093–1097. MR 2525780, DOI 10.1090/S0894-0347-08-00607-3
P. Erdös, On sets of distances of $n$ points, Amer. Math. Monthly 53 (1946), 248–250. MR 15796, DOI 10.2307/2305092
Larry Guth, The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263–286. MR 2746348, DOI 10.1007/s11511-010-0055-6
Larry Guth and Nets Hawk Katz, On the Erdős distinct distances problem in the plane, Ann. of Math. (2) 181 (2015), no. 1, 155–190. MR 3272924, DOI 10.4007/annals.2015.181.1.2
A. H. Stone and J. W. Tukey, Generalized “sandwich” theorems, Duke Math. J. 9 (1942), 356–359. MR 7036
Terence Tao, From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE, Notices Amer. Math. Soc. 48 (2001), no. 3, 294–303. MR 1820041
References
- Zeev Dvir, On the size of Kakeya sets in finite fields, J. Amer. Math. Soc. 22 (2009), no. 4, 1093–1097. MR 2525780, DOI 10.1090/S0894-0347-08-00607-3
- P. Erdős, On sets of distances of $n$ points, Amer. Math. Monthly 53 (1946), 248–250. MR 0015796, DOI 10.2307/2305092
- Larry Guth, The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263–286. MR 2746348, DOI 10.1007/s11511-010-0055-6
- Larry Guth and Nets Hawk Katz, On the Erdős distinct distances problem in the plane, Ann. of Math. (2) 181 (2015), no. 1, 155–190. MR 3272924, DOI 10.4007/annals.2015.181.1.2
- A. H. Stone and J. W. Tukey, Generalized “sandwich” theorems, Duke Math. J. 9 (1942), 356–359. MR 0007036
- Terence Tao, From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE, Notices Amer. Math. Soc. 48 (2001), no. 3, 294–303. MR 1820041
Review Information:
Reviewer:
Terence Tao
Affiliation:
Department of Mathematics, University of California, Los Angeles
Email:
tao@math.ucla.edu
Journal:
Bull. Amer. Math. Soc.
55 (2018), 103-107
DOI:
https://doi.org/10.1090/bull/1586
Published electronically:
August 8, 2017
Review copyright:
© Copyright 2017
American Mathematical Society
