EMSW21-RTG: Analysis and Differential Equations

这是芝加哥大学数学系为期一年的分析与微分方程研究训练小组（RTG）类型的项目。该项目资助研究生和访问学者，并组织针对数学、工程和科学领域的高级本科生、研究生和年轻博士后的暑期课程。分析和微分方程是数学的核心、深奥和丰富的领域。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。现代计算机性能的指数级提高使日益复杂的微分方程组的实际应用成为可能。虽然最近的成果解决了许多突出的问题，但仍有许多问题有待解决。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受过良好训练的年轻数学家的需求不断增长。pi和数学界的其他人认为，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。这个为期一年的项目的目标是为发展一个全面的现代教育计划提供种子，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，并提高未来数学科学家（在学术界或工业界工作）的培训质量。支持在这一领域工作的研究生将增加愿意从事应用分析工作的学生的数量。我们的期望是，提议的暑期课程将作为一种教育活动的模式，以吸引更多的研究人员研究微分方程，并教育工程和科学领域的学生和博士后。

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.