High-dimensional phenomena and asymptotic geometric analysis

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The proposed research program is in the area of Pure Mathematics called Asymptotic Geometric Analysis. This area -- by virtue of its general framework, techniques it uses and develops, and impact on related areas -- can be situated at the "crossroads" of many directions of mathematics. In particular, directions I plan to study in the next years are motivated, besides their intrinsic interest, by questions (and recent progress) in probability, Banach space theory, convex geometry, random matrix theory, asymptotic combinatorics and learning theory, among others. On the other hand, based on the present common experience, one can expect that solutions obtained within AGA may influence these other fields, leading to a fruitful mutual cross-fertilization.