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

这个RTG项目延续了密歇根大学在代数几何及其边界领域的一个成功的研究培训项目。目标受训者是最近的博士和高级研究生，尽管本科生也参与其中，但规模较小。该项目由五位资深教师（William Fulton, Robert Lazarsfeld, Mircea Mustata， Yongbin阮永斌和Karen Smith）与密歇根大学相关领域的另外16位资深教师共同负责。代数几何是当今数学的一个中心和高度活跃的分支，与其他数学和科学分支的联系日益重要。这些其他领域包括交换代数、数论、组合学、表示理论和复分析，以及弦理论和理论物理和计算机科学的其他方面。代数几何在20世纪末的爆炸性增长，使得这是一个非常令人兴奋的开始研究的时刻，但它也使年轻的研究人员很难起步。这个项目将增加在代数几何及其边界领域受过广泛训练的研究人员的流动。考虑到参与该项目的研究小组的规模和知名度，密歇根的代数几何RTG项目已经并将继续在国家层面上产生重大影响，在代数几何及其周围建立一个蓬勃发展的年轻研究人员社区。该项目开发了受训者的研究潜力，以及他们培养下一代的能力。活动包括丰富的研讨会和工作坊活动，包括博士后学员有机会在资深教师的指导下提出，设计和组织研讨会；博士后有机会在一名资深教师的指导下设计和领导本科生研究项目；为高级研究生和博士后提供大量机会，以发展他们的技术和说明性演讲技能，并在数学研究生涯的各个方面接受指导；资助实习生参加国内和国际会议，以便建立联系，接触密歇根大学没有代表的研究趋势，并在他们的工作演讲中获得知名度。

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.