Challenges in Geometry, Analysis and Computation: High Dimensional Synthesis

Yale University, New Haven CT

Investigators

Abstract

This award will provide support to defray expenses of participants, especially junior investigators, women and mathematicians from under-respresented groups in the sciences to attend the conference "Challenges in Geometry, Analysis and Computation: High Dimensional Synthesis" to be held at Yale University during June 4-6, 2012. The conference is motivated by the development in recent years of new powerful tools for overcoming the challenges associated with problems set in high dimensional spaces. These tools include compressive sensing, random projections, diffusion maps for parameterizing high-dimensional data sets, fast multipole methods, and many more. The premise of the meeting is that these different techniques share an intellectual heritage in a body of work originating from harmonic and functional analysis. A major problem confronting scientists nowadays is dealing with massive quantities of data. Over the last decades, the development of powerful computers has been very useful in treating many computational problems. Nonetheless severe limitations occur when the amount of data becomes too large. The interaction of Harmonic Analysis, Computational Mathematics, Combinatorial Geometry, Probability and Operator Theory has initiated a host of powerful methods to deal both with the processing and organizing of massive data sets, as well as efficient Numerical Analysis. More importantly they reveal new mathematical structures and open fundamental questions which need to be addressed, questions related to the analysis of functions in high dimensions, their sampling, effective descriptions, and approximations for efficient computability. Any further progress will have an enormous impact on our digital data driven world. The program for the conference features: (1) Lectures by leaders in the field. The conference will feature about 15 lectures by distinguished researchers . (2) Panel discussion on future directions. The conference will feature a panel discussion with some of the principal investigators from the major federal research agencies and national laboratories (ONR, DARPA, AFOSR, ARO, Livermore National Lab, Pacific Northwest Lab, Oak Ridge Laboratory) joined by Ronald R. Coifman, Peter W. Jones, Vladimir Rokhlin whose research influenced and laid much of the mathematical foundations of the field. The purpose is to identify fields of research that are likely to be both in demand by applications, and intellectually ripe for substantial progress. (3) Poster sessions. Younger researchers will be invited to present posters during the meeting with prime slots in the schedule reserved for poster sessions, and for a `poster blitz' presentation. A major goal of this conference is to educate the younger generation about critical needs in the analysis of data, important open problems and underlying areas of mathematical research. The scientific techniques under discussion are likely to have a profound impact on important applications. In particular help overcome key challenges in computing today and in the future (the "deluge of data" problem and the communication speed bottleneck). The involvement of young researchers will contribute to work force development in key STEM areas.