EMSW21-RTG: Developing American Research Leadership in Algebraic Geometry and its Boundaries

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This RTG project continues a successful research training program in algebraic geometry and its boundary areas at the University of Michigan. Target trainees are recent PhDs and advanced graduate students, though undergraduates are also involved on a smaller scale. The project is run by five senior faculty members (William Fulton, Robert Lazarsfeld, Mircea Mustata, Yongbin Ruan and Karen Smith) in consultation with an additional 16 senior faculty at Michigan in related areas. Algebraic geometry is a central and highly active branch of mathematics today, with increasingly important connections to other branches of mathematics and science. These other areas include commutative algebra, number theory, combinatorics, representation theory, and complex analysis, as well as string theory and other aspects of theoretical physics and computer science. The explosive growth of algebraic geometry at the end of the twentieth century has made this a very exciting time to begin research, but it has also made it difficult for young researchers to get started. This project will increase the flow of broadly trained researchers in algebraic geometry and its boundary areas. Given the size and visibility of the research groups involved in this project, Michigan's Algebraic Geometry RTG program has had and will continue to have a substantial impact at the national level in building a thriving community of young researchers in and around algebraic geometry. The project develops the research potential of its trainees, as well as their capability to nurture the next generation. Activities include a rich array of seminar and workshop activities, including the opportunity for post-doctoral trainees to propose, design and organize workshops under the mentorship of a senior faculty member; opportunities for post-doctoral researchers to design and lead undergraduate research projects under the mentorship of a senior faculty member; numerous opportunities for advanced graduate students and post-docs to develop their technical and expository lecturing skills, and to receive mentoring on all aspects of a research career in mathematics; funds for trainee travel to domestic and international conferences in order to establish connections, get exposure to research trends not represented at Michigan, and gain visibility as they lecture on their work.