RTG: Analysis and Differential Equations

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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.