Discrete geometry and extremal combinatorics of hypergraphs

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We studied some concrete problems in discrete geometry and extremal combinatorics using tools coming from different branches of mathematics. We have obtained results on "sphere-systems in Euclidean spaces," "large regular simplices contained in a hypercube," "extension of the Erdos-Ko-Rado theorem on t-intersecting families," "convex bodies fixed by planar frames," and so on.