Discrete analogues of Kakeya problems

Doctoral thesis, Preprint English OPEN
Iliopoulou, Marina;
(2013)
  • Publisher: The University of Edinburgh
  • Subject: algebraic curves | Mathematics - Combinatorics | joints problem | Mathematics - Classical Analysis and ODEs | Mathematics - Algebraic Geometry | Kakeya problem

This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider discrete analogues of the maximal Kakeya operator conjecture and of the recently solved en... View more
  • References (4)

    6 Transversality of more general curves 77 6.1 Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2 Multijoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 L. Guth, 'The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture', Acta Mathematica 205 (2010) 263-286.

    L. Guth, N. H. Katz, 'Algebraic Methods in Discrete Analogs of the Kakeya Problem', Adv. Math. 225, no. 5 (2010) 2828-2839.

    L. Guth, N. H. Katz, 'On the Erd˝os distinct distance problem in the plane', arXiv:1011.4105v3 (2010).

    M. Iliopoulou, 'Counting joints with multiplicities', Proceedings of the London Mathematical Society 106, no. 3 (2013) 675-702 [KMS11] H. Kaplan, J. Matouˇsek, M. Sharir, 'Simple Proofs of Classical Theorems in Discrete Geometry via the Guth-Katz Polynomial Partitioning Technique', Discrete Comput. Geom. 48, no. 3 (2012) 499-517.

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