High-dimensional phenomena and asymptotic geometric analysis

高维现象和渐近几何分析

• 批准号: 8854-2008
• 负责人: TomczakJaegermann, Nicole
• 金额: $ 3.5万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=389849
• 关键词: dimensional; phenomena; asymptotic; geometric; analysis

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.

拟议的研究计划是在纯数学领域称为渐近几何分析。 这一领域-凭借其总体框架，它使用和发展的技术，以及对相关领域的影响-可以位于数学许多方向的“十字路口”。 特别是，方向我计划在未来几年的研究动机，除了他们的内在利益，问题（和最近的进展）在概率，Banach空间理论，凸几何，随机矩阵理论，渐近组合学和学习理论，等等。 另一方面，根据目前的共同经验，人们可以预期，在阿加内获得的解决办法可能会影响这些其他领域，导致富有成效的相互交流。