RTG: Geometry and Topology at Princeton

点击翻译按钮获取中文摘要

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.