High-dimensional phenomena and asymptotic geometric analysis

拟议的研究计划是在被称为渐近几何分析的纯数学领域。这一领域--凭借其总体框架、所使用和开发的技术以及对相关领域的影响--可以位于许多数学方向的“十字路口”。特别是，我计划在未来几年研究的方向，除了内在的兴趣之外，还受到概率、Banach空间理论、凸几何、随机矩阵理论、渐近组合学和学习理论等方面的问题(和最近的进展)的推动。另一方面，根据目前的共同经验，人们可以预期，在AGA内获得的解决方案可能会影响这些其他领域，从而导致富有成效的相互受精。

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.