EMSW21-RTG: Analysis and Differential Equations

EMSW21-RTG：分析和微分方程

• 批准号: 1044944
• 负责人: Panagiotis Souganidis
• 金额: $ 10万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1044944&HistoricalAwards=false
• 关键词: EMSW21; RTG; Analysis; Differential; Equations

This is a one year Research Training Group (RTG) type of project in Analysis and Differential Equations at the Department of Mathematics of the University of Chicago. The project funds graduate students and visitors and the organization of a summer course aimed towards advanced undergraduates, graduate students and young postdocs in mathematics, engineering and sciences. 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 are the basic theoretical tools in 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 along with others in the mathematical community believe that there is a severe shortage of US PhDs trained in (applied) analysis and differential equations. The goal of the proposed one year project is to provide the seed towards developing a well-rounded and modern educational program to increase the number of American researchers working in the applied analysis and differential equations and to improve the quality of the training of future mathematical scientists (working in either academia or industry). Having support for graduate students working in this general area will increase the number of students willing to work in applied analysis. The expectation is that the proposed summer course will serve as a model of the type of educational activity needed to attract more researchers to differential equations as well as to educate student and postdocs in engineering and sciences.

这是一个为期一年的研究培训组（RTG）类型的项目在分析和微分方程在数学系的芝加哥大学。该项目资助研究生和来访者，并为数学、工程和科学领域的高年级本科生、研究生和年轻博士后组织暑期课程。分析和微分方程是数学的中心、深刻和丰富的领域。 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现象，是科学和技术的基本理论工具。现代计算机能力的指数级提高使得越来越复杂的微分方程系统能够得到实际应用。虽然最近的成果解决了许多悬而未决的问题，但许多问题仍然悬而未决。理解这些模型的数学性质是必不可少的。学术界和工业界对这些领域年轻、训练有素的数学家的需求不断增长。PI沿着其他数学界人士认为，在（应用）分析和微分方程方面受过训练的美国博士严重短缺。拟议的为期一年的项目的目标是提供种子朝着发展一个全面和现代化的教育计划，以增加美国研究人员在应用分析和微分方程工作的数量，并提高未来的数学科学家的培训质量（无论是在学术界或工业界工作）。支持研究生在这一领域的工作将增加愿意在应用分析工作的学生人数。预期的是，拟议的暑期课程将作为教育活动的类型需要吸引更多的研究人员微分方程以及教育学生和博士后在工程和科学的模型。