RTG: Geometry and Topology at Princeton

近年来，几何学和低维拓扑学领域经历了一个快速发展的时期，这是由于新发现的相互作用，无论是相互之间还是与其他广泛的数学学科。 这种令人兴奋的思想融合导致了数学中新的意外现象的发现，解决了一些长期存在的问题，并为未来提出了新的挑战。几何和拓扑学研究培训补助金在普林斯顿代表了一个广泛的数学家在普林斯顿的合作努力，以帮助培养下一代的数学家-本科生，研究生和博士后-在这些令人兴奋的发展，以帮助他们准备贡献进一步的进步。该项目的组成部分包括本科生培训和研究机会，以及研究生和博士后研究人员在研究和教学方面的指导。该补助金包括密集的夏季课程，本科课程和研讨会的发展，研究生支持，研究和工作研讨会的支持，访问者的资金和博士后研究职位。RTG代表了普林斯顿大学12个几何学家和拓扑学家的共同努力。这个小组的研究包括低维拓扑、辛几何、接触几何、共形几何和几何分析。 该项目将包括：（1）暑期研究机会，从教师密切指导本科生;（2）在该领域每年6名研究生全额资助;（3）支持两名博士后研究助理，其教学和研究将由教师积极指导;（4）三个密集的暑期课程，本科生和研究生将介绍拓扑和几何的最新发展;（5）在夏季课程的高潮三个主要会议;（6）引进新的本科和研究生课程;（7）一些研究研讨会和学生工作研讨会;和（8）额外的讲座，旨在让学生在数学一般和拓扑/几何具体。

In recent years, the areas of geometry and low-dimensional topology have experienced a period of rapid growth, owing to new-found interactions, both with each other and with a wide array of other mathematical disciplines. This exciting blend of ideas has led to the discovery of new unexpected phenomena in mathematics, settling some long-standing questions, and raising new challenges for the future. The geometry and topology research training grant at Princeton represents a collaborative effort of a broad group of mathematicians at Princeton to help train the next generation of mathematicians -- undergraduates, graduate students, and post-docs -- in these exciting developments, so to help prepare them to contribute further advances. Components of this project include undergraduate training and research opportunities, and mentoring of graduate students and post-doctoral researchers in both research and teaching. The grant includes intensive summer courses, development of undergraduate courses and seminars, graduate support, support for research and working seminars, funds for visitors, and post-doctoral research positions.The RTG represents the combined effort of twelve geometers and topologists at Princeton University. The research represented in this group includes low-dimensional topology, symplectic geometry, contact geometry, conformal geometry, and geometric analysis. The project will include: (1) summer research opportunities for undergraduates with close mentoring from faculty; (2) full funding for 6 graduate students per year in the field; (3) support for two post-doctoral research associates, whose teaching and research will be actively mentored by the faculty; (4) three intensive summer programs, where undergraduates and graduate students will be introduced to recent developments in topology and geometry; (5) three major conferences at the culmination of the summer programs; (6) the introduction of new undergraduate and graduate courses; (7) a number of research seminars and student working seminars; and (8) additional lectures aimed at engaging students in mathematics in general and in topology/geometry specifically.