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The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry is an extremely active area of research: the participation of a considerable number of talented young mathematicians at this meeting is testament to the fact that the field is flourishing.
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Keith M. Ball, Martin Henk, Monika Ludwig, Convex Geometry and its Applications. Oberwolfach Rep. 9 (2012), no. 4, pp. 3473–3548