Constructive Approximation and Harmonic Analysis

该奖项为2016年3月至7月在西班牙巴塞罗那数学研究中心（CRM）举行的“建设性逼近与谐波分析”密集研究项目的美国参与者（包括年轻研究人员和知名科学家）提供资金。该计划将集中在谐波分析和近似理论领域，数学领域的基础表示和近似函数和数据。重点将放在建设性的高维逼近和表示方法上。最近，在工程、生物、医学和其他科学领域的应用推动下，出现了新的具有挑战性的问题。这些问题的一个共同特征是，它们涉及到极高维度的数据和多变量函数，在这种情况下，经典的近似方法不能很好地工作。这是数学中一个重要而迅速发展的领域。最近在谐波分析和近似理论的界面上活动的增加使得一个强调这种相互作用的研究计划的时机完美，并将有助于这两个领域的交叉施肥。CRM是一个著名的数学研究机构，为这样的项目提供了良好的设施，调和分析和近似理论在CRM的活动中一直有很强的代表性。该项目将包括“函数空间与高维逼近”研讨会（2016年5月），针对研究生和博士后的“构造逼近与谐波分析方法”高级课程（2016年5 - 6月），以及“谐波分析与逼近理论”会议（HAAT 2016, 2016年6月）。此外，将有充足的时间进行合作研究。该项目将汇集分析和数值分析领域的不同数学家团体，试图在高维问题上取得突破，这在数据压缩和处理（对信息技术应用和医学成像至关重要）中非常重要。这一领域的进展将影响其他几个数学科学领域，包括信号和图像处理、数值数学、学习理论和优化理论。该计划的活动日程与欧洲和美国在这些领域的其他活动进行了精心协调，这将允许大量的美国数学家参加。会议的网址是http://www.crm.cat/en/Activities/Curs_2015-2016/Pages/IRP-Approximation-and-Harmonic-Analysis.aspx

This award provides funding to defray expenses of US-based participants (both young researchers and established scientists) in the intensive research program "Constructive Approximation and Harmonic Analysis", which is to be held at the Centre de Recerca Matematica (CRM) in Barcelona, Spain during the period of March-July, 2016. This program will concentrate on the areas of harmonic analysis and approximation theory, areas of mathematics that underlie the representation and approximation of functions and data. The emphasis will be put on constructive high-dimensional methods of approximation and representation. Recently, driven by applications in engineering, biology, medicine, and other areas of science, new challenging problems have appeared. A common feature of many of these problems is that they involve data and multivariable functions in extremely high dimensions, in which setting classical methods of approximation do not work well. This is an important and rapidly developing area of mathematics. A recent increase of activity at the interface of harmonic analysis and approximation theory makes the timing perfect for a research program that emphasizes this interplay and will help the cross fertilization of both fields. CRM is a renowned mathematics research institute which provides excellent facilities for such a program, and both harmonic analysis and approximation theory have historically been strongly represented in the activities of CRM.The program will include a workshop on "Function Spaces and High-Dimensional Approximation" (May 2016), several advanced courses on "Methods of Constructive Approximation and Harmonic Analysis" aimed at graduate students and postdocs (May-June 2016), and a Conference on "Harmonic Analysis and Approximation Theory" (HAAT 2016, June 2016). In addition there will be ample time for collaborative research. The program will bring together different groups of mathematicians working in several areas of analysis and numerical analysis to try to make a breakthrough in high-dimensional problems, which are very important in data compression and processing (critical to information technology applications and medical imaging). Progress in this area will impact several other mathematical sciences communities, including signal and image processing, numerical mathematics, learning theory, and optimization theory. The schedule of the events in the program has been carefully coordinated with other European and US events in these fields, which will allow a large number of US-based mathematicians to participate. The web site for the conference is http://www.crm.cat/en/Activities/Curs_2015-2016/Pages/IRP-Approximation-and-Harmonic-Analysis.aspx