LECTURES ON DISCRETE GEOMETRY (Graduate Texts in Mathematics 212) By JI MATOUEK: 481 pp., 31.50 (US$39.95), ISBN 0-387-95374-4 (Springer, New York, 2002).

By Imre Brny. 2003

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Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture (2007, background): “See, for example, a monograph by Matousek ([16]) and the references contained therein to review the main milestones of the progress towards this conjecture.”
Error correction via linear programming (2005, methodology): “For instance , by using concentration of measure inequalities and the Marchenko-Pastur law [39] as in [11, Theorem 1.6] (see also [22] [35] [44] for some relevant results) one can establish Theorem 1.2.”
Erdös distance problem in vector spaces over finite fields (2005, unknown): “5.1 Proof of Theorem 1.13 and Theorem 1.7 . . . . . . . . . . . . . . . . . . . . 11 5.2 Proof of Theorem 1.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6 Non-Salem sets and the behavior of the Mattila integral 14”
Complex Interpolation between Hilbert, Banach and Operator spaces (2008, unknown): “We have then a fortiori:”