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Period17 Dec - 23 Dec 2006
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, both the discrete and convex branches of it, has experienced a striking series of developments in the past 5 years. Several examples were presented at this meeting, for example the work of Naor on the non-linear Dvoretzky theorem, that of Paouris on the distribution of the Euclidean norm on a convex domain and the results of Rudelson on the singular values of random matrices.