RTG: Enhancing American Research Leadership in Geometry

数学创新往往源于物理学思想和传统数学思想的相互作用。然而，对于一个领域的研究人员来说，理解另一个领域的想法和进展变得越来越困难。这个项目的目的是在传统数学系和致力于数学和理论物理之间相互作用的研究中心合作培养年轻的数学家。我们的目标是培养下一代数学家，他们既有在自己选择的领域取得成功的工具，也有必要的设施来弥合地区之间的差距。这个项目将建立一个几何研究培训小组，作为石溪数学系和西蒙斯几何和物理中心的合作努力。它将在传统数学系培养年轻数学家的长期承诺与隔壁一个主要国际研究中心提供的特殊科学机会结合在一起。该计划的总体目标是培养一批年轻的数学家，他们将结合特定几何领域的专业知识，认真欣赏几何的其他子领域，以及几何和数学物理之间的联系。RTG将由三个主要组成部分组成。它将资助9名博士后研究员，他们将是数学系和西蒙斯中心的正式参与成员。除了从事全面的传统数学活动外，研究员还将参加联合研讨会，汇聚数学和理论物理方面的博士后。该方案还将为一批数学研究生提供部分支持，他们将加入西蒙斯中心，并将全面参与该中心的活动。最后，该计划将推出一些新的活动，旨在丰富石溪数学本科生的经验，包括那些对教学生涯感兴趣的人，并将他们介绍给西蒙斯中心的科学焦点。

Mathematical innovations often arise from the interplay between ideas from physics and from traditional mathematics. However, it has become increasingly difficult for researchers in one field to understand the ideas and advances in the other. The purpose of this program is to train young mathematicians collaboratively at a traditional mathematics department and at a research center devoted to the interactions between mathematics and theoretical physics. The goal is produce mathematicians of the next generation who will have both the tools to succeed in their chosen fields and the facility necessary to bridge the gap between areas.This project will establish a Research Training Group in geometry as a collaborative effort between the Stony Brook Mathematics Department and the Simons Center for Geometry and Physics. It unites a long commitment to training young mathematicians at a traditional mathematics department with the exceptional scientific opportunities presented by a major international research center located next door. The overall aim of the program is to train a group of young mathematicians who will combine expertise in a specific geometric field with a serious appreciation of the other subfields of geometry and of the connections between geometry and mathematical physics. The RTG will have three main components. It will fund nine Postdoctoral Fellows who will be full participating members of both the mathematics department and the Simons Center. Besides engaging in a full range of traditional mathematical activities, the Fellows will participate in joint seminars bringing together postdocs in mathematics and theoretical physics. The program will also provide partial support to a cadre of graduate trainees in mathematics, who will have an affiliation in the Simons Center and will participate fully in activities in the Center. Finally, the program will put in place a number of new activities designed to enrich the experiences of Stony Brook mathematics undergraduates, including those interested in teaching careers, and to introduce them to the scientific focus of the Simons Center.