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.

这是芝加哥大学数学系的RTG项目``分析和差异方程式''的一项建议。五个共同案例（Csornyei，Fefferman，Kenig，Schlag和Souganidis）在学年中提出了几项活动，该活动涉及研究生不足的学生和研究生和较小的学生和差异方程。透视，微分方程是所有科学和工程的最基本模型。这些模型是必不可少的。在这些领域，年轻，训练有素的数学家的学术界和行业的需求一直在增长。PIS认为，在（应用）分析和微分方程中培训的美国博士学位非常短缺。拟议的项目的核心目标是制定一项全面且现代的教育计划，以增加在应用分析和微分方程中工作的美国研究人员的数量，并提高未来数学科学家（在学术界或行业工作）的培训质量，从本科数学专业的专业专业的大满贯。 PI预计该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，本科研究经验和为期四个星期的夏季教程/课程）将成为全国类似举措的典范。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定基础，而且还可以通过几项计划的活动为这些发展的数学领域之间的现代联系做好准备。为了成为学术界或行业中应用数学的成功研究者，绝对需要这种多元化的培训。借助RTG资助，芝加哥大学的PIS和其他研究人员将刺激形成，形成和发展环境的环境，在这种环境中，成功利用本科生和研究生，博士后家伙和教职员工的合并才能的活动更为突出。拟议的项目旨在将芝加哥大学的伟大传统带到分析中，以更新高度。 PIS的整个活动都认为，该计划具有成为当地和国家培训和分析和微分方程研究范围的潜力。