Challenges in Geometry, Analysis and Computation: High Dimensional Synthesis

该奖项将为参加2012年6月4日至6日在耶鲁大学举行的“几何、分析和计算的挑战：高维综合”会议的参与者，特别是来自科学领域代表性不足群体的初级研究人员、女性和数学家提供费用支持。会议的动机是近年来开发的新的强大工具，用于克服与高维空间问题相关的挑战。这些工具包括压缩感知、随机投影、用于参数化高维数据集的扩散图、快速多极方法等等。会议的前提是，这些不同的技术在源自和谐和功能分析的工作中共享知识遗产。当今科学家面临的一个主要问题是处理大量的数据。在过去的几十年里，强大的计算机的发展在处理许多计算问题方面非常有用。然而，当数据量过大时，就会出现严重的限制。谐波分析、计算数学、组合几何、概率论和算符理论的相互作用，开创了一系列强大的方法来处理和组织大量数据集，以及高效的数值分析。更重要的是，它们揭示了新的数学结构，并提出了一些需要解决的基本问题，这些问题与高维函数的分析、它们的采样、有效描述和高效可计算性的近似有关。任何进一步的进展都将对我们这个数字数据驱动的世界产生巨大影响。会议安排的主要特点是：(1)由该领域的领导者进行演讲。这次会议将有15个杰出的研究人员的演讲。(2)小组讨论未来发展方向。会议将与来自主要联邦研究机构和国家实验室（ONR， DARPA， AFOSR， ARO，利弗莫尔国家实验室，太平洋西北实验室，橡树岭实验室）的一些主要研究人员进行小组讨论，Ronald R. Coifman, Peter W. Jones， Vladimir Rokhlin的研究影响并奠定了该领域的许多数学基础。目的是确定那些既可能被应用需求，又可能在智力上成熟到可以取得实质性进展的研究领域。(3)海报环节。年轻的研究人员将被邀请在会议期间展示海报，并在日程安排的主要时段保留海报会议和“海报闪电战”展示。这次会议的一个主要目标是教育年轻一代关于数据分析的关键需求，重要的开放问题和数学研究的潜在领域。正在讨论的科学技术可能对重要的应用产生深远的影响。特别是帮助克服当今和未来计算中的关键挑战（“数据泛滥”问题和通信速度瓶颈）。年轻研究人员的参与将有助于关键STEM领域的劳动力发展。

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.