Asymptotic geometric analysis, random matrices and related topics

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The project concentrates on several related directions of Asymptotic Geometric Analysis (AGA). This field is concerned with geometric and linear properties of finite dimensional objects, such as convex sets and normed spaces, especially with the characteristic behavior that emerges when the dimension, or a number of other relevant free parameters, is suitably large or tends to infinity. High-dimensional systems are very frequent in mathematics and applied sciences, hence, understanding high-dimensional phenomena is becoming increasingly important. The last decade has seen a tremendous growth of AGA, with the development of new powerful techniques, mainly of probabilistic nature. By virtue of AGA's general framework, methods, and its impact on related fields, AGA can be situated at the "crossroads" of many branches of mathematics: functional analysis, convex and discrete geometry, and several areas of probability.