From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE

Details From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE

2000-08-14

arxiv.org/abs/math/0008098v1

Mathematics

Classical Analysis and ODEs

32 pages, 9 figures, submitted, Notices Amer. Math. Soc. (The published version is likely to be substantially shorter)

Scientific paper

We survey the interconnections between geometric combinatorics (such as the Kakeya problem), arithmetic combinatorics (such as the classical problem of determining which sets contain arithmetic progressions), oscillatory integrals (such as the Bochner-Riesz, restriction, and local smoothing problems), and the local and global well-posedness theory for non-linear dispersive and wave equations.

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