ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ - ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ
Λεωφ. Κνωσού, 714 09 Ηράκλειο. Τηλ: +30 2810393800, Fax +30 2810393881
We shall use combinatorial and analytic methods to prover results of the following type. If a subset of a vector space is sufficiently large, in terms of size in the discrete case, of Hausdorff dimension in the continuous case, the set of all possible finite point configurations determined by this set is a positive proportion, in the appropriate sense, of all the possible finite point configurations of a given size. Connections with sum-product theorems in additive number theory, restriction theory in harmonic analysis and ergodic theory in the context of finite point configurations will also be discussed.
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