EMSW21-RTG: Geometric, Topological and Statistical Methods for Analyzing Massive Datasets

在过去的十年中，大量的，高维的，时变的数据集的分析已经成为一个重要的问题，大量的科学家和工程师。 研究人员在研究截然不同的问题时，对几个学科的观察表明，许多数据集中存在几何和拓扑结构，目前的许多研究都致力于建模和利用这些结构来帮助预测和信息提取。最近的研究工作，除其他外，已经表明，整合统计方法与来自计算拓扑学和扩散几何学的想法往往会导致显着的上级的结果比传统的手段。研究人员现在建议将这些方法纳入数学/统计课程和部门结构中，通过建立本科生和研究生研究和教育的垂直整合计划。这项活动得到了数学科学部内项目的广泛支持，包括应用数学，计算数学，统计学和拓扑学项目，以及数学科学劳动力项目部。这涉及核心理论领域的新本科课程，研究生主题课程，本科生广泛的暑期研究项目，以及针对研究生和本科生的为期一年的研讨会。 此外，研究人员将通过针对小型大学教师的夏季研讨会和针对其他大型研究机构教师的方法论研讨会传播他们的想法。分析大量复杂数据的需求出现在具有国家重要性的各种科学领域，包括例如卫星图像分析，医学基因组学，和互联网安全。调查人员提出了一个培训未来数学科学家攻击这些新类型问题的计划。该计划将垂直整合，促进博士后，本科生和研究生以及高级教师之间的广泛合作，并将包括理论课程和实践研究活动的动态混合。该计划的参与者将获得宝贵的专业经验，以在工业和学术就业市场中脱颖而出。

In the past decade, the analysis of massive, high-dimensional, time-varying data sets has become a critical issue for a large number of scientists and engineers. Observations across several disciplines, by researchers studying dramatically different problems, suggest the existence of geometrical and topological structures in many data sets, and much current research is devoted to modeling and exploiting these structures to aid in prediction and information extraction. Recent work by the investigators, among others, has shown that integrating statistical methodologies with ideas derived from computational topology and diffusion geometry often leads to strikingly superior results than by conventional means. The investigators now propose to bring these methods into the mathematics/statistics curriculum and departmental structure in a formal way, by establishing a vertically integrated program of undergraduate and graduate research and education. This activity has broad support from programs within the Division of Mathematical Sciences, including Applied Mathematics, Computational Mathematics, Statistics and Topology programs, as well as Division of Mathematical Sciences Workforce Program.This involves new undergraduate courses in the core theoretical areas, graduate topics courses, an extensive summer research program for undergraduates, as well as year long seminars aimed at both graduate and undergraduate students. In addition, the investigators will disseminate their ideas via summer workshops aimed at small-college faculty, and methodology workshops directed to faculty from other large research institutions.The need to analyze massive, complex data arises in a wide variety of scientific areas of national importance, including for example satellite image analysis, medical genomics, and internet security.The investigators propose a program of training future mathematical scientists to attack these new types of problems. The program will be vertically integrated, fostering extensive collaboration between post-docs, undergraduate and graduate students, and senior faculty, and will comprise a dynamic mixture of theoretical coursework and hands-on research activity. Participants in the program will gain valuable professional experience to distinguish them in the industrial and academic job-market.