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.
The award provided partial funding to support junior investigators and mathematicians from under represented groups in the sciences (especially women and minority researchers from the United States) to attend the conference Challenges in Geometry, Analysis and Computation: High Dimensional Synthesis that was held at Yale University on June 3 - 6, 2012. The intellectual motivation for the conference was the development in recent years of new powerful tools for overcoming the challenges associated with problems set in high dimensional spaces. Such techniques are needed, e.g., in order to efficiently and accurately extract useful information from massive data sets, and also for performing simulations of phenomena such as acoustic and electro-magnetic scattering, and medical imaging. These tools are known in the mathematics community by names such as compressive sensing, random projections, diffusion maps for parameterizing high-dimensional data sets, fast multipole methods, and many more. The conference program included the following items: 15 plenary lectures: The lecturers included several distinguished researchers, including several members of the national academies, a Fields medalist, a Waterman Award recipient, a MacArthur fellow, winners of the Von Neumann and Steele prizes. A panel discussion on future directions: Academic scientists who laid the mathematical foundations of the field joined seven program directors and scientistss from the major federal agencies and national laboratories (ONR, DARPA, AFOSR, US Army-ARO, Livermore National Lab, Pacific Northwest Lab, Oak Ridge Lab) for a panel discussion on future directions, and the research needs of federal agencies. Poster sessions: More than 40 young researchers presented posters during the meeting, and some were also given a chance to present to the entire meeting in a ``poster blitz'' session. The program also included several social activities, and was overall designed to give junior participants ample opportunities to interact with each other and with senior participants. To maximally leverage the impact of the meeting, all lectures were recorded with both audio and video; and the slides from the talks have been posted on the conference website.
