University of Pennsylvania RTG in Mathematical Physics

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This project vertically integrates research and training in Mathematical Physics, Geometry, and String Theory at the Mathematics Department of the University of Pennsylvania. The Penn group will undertake a series of training activities including graduate summer schools, research and outreach workshops, the development of new graduate and undergraduate courses, and preparation of course materials, including a graduate textbook. In parallel, three vertical research projects will be developed: the exciting new connections between the Geometric Langlands Program and dualities in quantum field theory and string theory; a geometric and numerical investigation of the action of the renormalization group flow on the moduli of supersymmetric quantum field theories; and an exploration of special holonomy metrics. The group will create a fertile educational environment that will introduce US students of various preparation levels to cutting edge research questions in the mathematical aspects of high energy physics.Mathematical Physics is one of the most active branches of mathematics and physics today, with increasingly important connections to other branches of mathematics and science. The project activities are designed to increase the number and the diversity of Americans who are actively exploring Mathematical Physics, Geometry, and String Theory, and to improve the quality of their experience. Strong improvements are anticipated at all levels, with very significant improvements in graduate and postdoctoral research.. The explosive growth of interest in the theory of universe has made this a very exciting time to begin research in the field, but it has also made it difficult for young researchers to get started. This project will increase the flow of broadly trained researchers in Mathematical Physics, Geometry, and String Theory, therefore enhancing the training infrastructure and the research workforce in these vital areas of mathematics in the twenty-first century.