Constructive Approximation and Harmonic Analysis

University Of South Carolina At Columbia, Columbia SC

Investigators

Abstract

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