RTG: Analysis and Differential Equations

RTG：分析和微分方程

• 批准号: 1246999
• 负责人: Panagiotis Souganidis
• 金额: $ 250万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-06-15 至 2020-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1246999&HistoricalAwards=false
• 关键词: RTG; Analysis; Differential; Equations

This is a proposal for an RTG project in ``Analysis and Differential Equations" at the Department of Mathematics of the University of Chicago. The five co-PIs (Csornyei, Fefferman, Kenig, Schlag and Souganidis) propose several activities during the academic year geared towards undergraduate and graduate students and postdocs. Analysis and differential equations are central, deep and rich fields of mathematics. From an applied perspective, differential equations are the most fundamental mathematical models in all of science and engineering. They describe phenomena from quantum mechanics to weather prediction and climate,and generally speaking constitute the basic theoretical tools for much of science and technology. The exponential improvement in the capabilities of modern computers allows for the practical use of increasingly complex systems of differential equations. Although recent results have solved numerous outstanding problems, many still remain open. The understanding of the mathematical properties of these models is essential. The need in both academia and industry for young, well-trained mathematicians in these areas is ever growing.The PIs believe that there is a severe shortage of US PhDs trained in (applied) analysis and differential equations. The proposed project's central goals are to develop a well-rounded and modern educational program to increase the number of American researcher working in the applied analysis and differential equations, and to improve the quality of training of future mathematical scientists (working in either academia or industry) from undergraduate mathematics majors to postdoctoral researchers. The PIs expect that the several components of this program (curriculum reform, new courses, integrated seminars, outreach activities, undergraduate research experience and four week long summer tutorials/courses) will serve as a model for similar initiatives across the country. The proposed project will not only provide aspiring mathematical scientists with a firm grounding in analysis and differential equations, but also prepare them for possible modern connections among these ever developing areas of mathematics through several planned activities. This diversified training is definitely needed in order to become a successful researcher in applied mathematics in either academia or industry. With the aid of the RTG funding, the PIs and other researchers at the University of Chicago will stimulate the formation and the formation and the development of an environment in which activities that successfully exploit the combined talents of undergraduate and graduate students, postdoctoral fellows and faculty members are more prominent features. The proposed project is aiming towards bringing the great tradition of the University of Chicago in analysis to renewed heights. Running the whole spectrum of activities the PIs believe that the program has the potential of becoming both a local as well as a national paradigm of training and research in analysis and differential equations.

这是一份芝加哥大学数学系“分析与微分方程式”RTG项目的建议书。五个共同绩效指标(Csornyei、Fefferman、Kenig、Schlag和Souganidis)提议在学年期间针对本科生、研究生和博士后开展几项活动。分析和微分方程式是数学的中心、深层和丰富的领域。从应用的角度来看，微分方程是所有科学和工程中最基本的数学模型。它们描述了从量子力学到天气预报和气候的各种现象，总的来说，它们构成了许多科学和技术的基本理论工具。现代计算机能力的指数级改进使日益复杂的微分方程组得以实际应用。尽管最近的成果解决了许多突出问题，但仍有许多问题有待解决。对这些模型的数学性质的理解是至关重要的。学术界和工业界对这些领域训练有素的年轻数学家的需求在不断增长。PI认为，受过(应用)分析和微分方程式培训的美国博士严重短缺。拟议中的项目的中心目标是开发一个全面的现代教育计划，以增加在应用分析和微分方程领域工作的美国研究人员的数量，并提高从本科生数学专业到博士后研究人员的未来数学科学家(在学术界或行业工作)的培训质量。PIS预计，这一计划的几个组成部分(课程改革、新课程、综合研讨会、外展活动、本科生研究经验和为期四周的暑期辅导/课程)将成为全国类似倡议的典范。拟议的项目不仅将为有抱负的数学科学家提供分析和微分方程方面的坚实基础，而且还将通过几个有计划的活动，使他们为这些不断发展的数学领域之间可能的现代联系做好准备。无论是在学术界还是产业界，要想成为一名成功的应用数学研究者，这种多样化的培训肯定是必要的。在RTG资金的帮助下，芝加哥大学的PI和其他研究人员将刺激形成和形成一种环境，在这种环境中，成功地开发本科生和研究生、博士后研究员和教职员工的组合人才的活动是更突出的特点。这项拟议的项目旨在将芝加哥大学在分析方面的伟大传统推向新的高度。在整个活动范围内，私人投资机构相信，该方案有可能成为分析和微分方程式方面的培训和研究的一个地方和国家范例。