Asymptotic geometric analysis, random matrices and related topics

该项目集中于渐近几何分析(AGA)的几个相关方向。这个领域涉及有限维对象的几何和线性性质，例如凸集和赋范空间，特别是当维度或一些其他相关的自由参数适当大或趋于无穷大时出现的特征行为。高维系统在数学和应用科学中非常常见，因此，理解高维现象变得越来越重要。在过去的十年中，随着新的强大的技术的发展，AGA有了巨大的增长，主要是概率性质的。由于AGA的一般框架、方法及其对相关领域的影响，AGA可以位于许多数学分支的“十字路口”：泛函分析、凸几何和离散几何，以及几个概率领域。

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.