NSF/CBMS Regional Conference in the Mathematical Sciences-"Probabilistic and Combinatorial Approach in Analysis"

NSF/CBMS 数学科学区域会议 - “分析中的概率和组合方法”

• 批准号: 0532494
• 负责人: Artem Zvavitch
• 金额: $ 3.25万
• 依托单位: Kent State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-15 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532494&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

At various times, probabilistic and combinatorial techniques have led to important advances in functional and harmonic analysis. In many situations, explicit constructions have proved elusive, but it has been possible to show that phenomena occur with high probability when certain parameters are varied randomly. At othertimes when explicit constructions have been beyond reach, combinatorial techniques have been applied effectively to provide existence proofs. Recently, these two types of approach have been used together to great effect in establishing new results in convex geometry, geometrical functional analysis and the theory oflarge matrices, as well as in signal processing and learning theory. Conversely, several important problems in probability, especially in the theory of random processes, have been solved using methods of geometric functional analysis. A window of opportunity has opened for the organization of an influential CBMS conference on probabilistic and combinatorial methods in functional analysis at Kent State University. Professor Mark Rudelson, one of the leading experts in the subject, has agreed to serve as the Principal Lecturer of the conference.

在不同时期，概率和组合技术导致了重要的进展，在功能和谐波分析。在许多情况下，显式构造被证明是难以捉摸的，但当某些参数随机变化时，现象发生的可能性很高。在其他时候，当显式构造无法实现时，组合技术已被有效地应用于提供存在性证明。近年来，这两种方法在凸几何、几何泛函分析、大矩阵理论以及信号处理和学习理论中得到了广泛的应用。相反，概率论中的几个重要问题，特别是随机过程理论中的问题，已经用几何泛函分析的方法解决了。一个窗口的机会已经打开了一个有影响力的CBMS会议的概率和组合方法在功能分析在肯特州立大学的组织。 Mark Rudelson教授是该主题的主要专家之一，已同意担任会议的首席讲师。