RTG: Geometry and Topology

该奖项为加州大学伯克利分校几何和拓扑研究训练组（RTG）的参与者提供了持续的支持。该项目将由六名教师（Ian Agol, Denis Auroux, Michael Hutchings, John Lott， Peter Teichner和Constantin Teleman）领导，他们将与数学系的其他成员合作，通过进一步加强对本科生，研究生和博士后的培训，在之前RTG项目的成功基础上再生产。前一个项目纳入了许多加强培训的机制，其中一些机制比其他机制效果更好。该小组将扩展成功的机制，并尝试后续创新。随着几何学和拓扑学变得越来越多面化和技术化，学生很难获得他们所需要的研究工具。该研究小组的活动将惠及所有层次的受训者，首先是大力招募本科生参与研究，继续举办研讨会和热门话题课程，以培训研究生掌握最新技术，最后包括指导帮助博士后开始他们的研究生涯。提供此类培训的机制将包括研究生授课的本科生研究课程，研究生在高级教师指导下的暑期本科生研究项目，博士后本科生指导，研究生及其他人员的背景研讨会，几何和拓扑座谈会，高级教师讲授的热点课程，博士后讲授的暑期研究生研讨会，以及以及与波恩马克斯-普朗克研究所的交换项目。该项目将涉及大约三名博士后助理，每年12名研究生，每个本科研究项目的12名本科生，以及每个夏季研究生研讨会的30名参与者。拟议的培训活动将直接或间接地增加美国公民和永久居民进入和继续从事数学研究的人数：直接通过招募和支持小组中的受训人员，间接通过建立可以在其他地方模仿的研究培训模式。

This award provides continued support for participants in the research training group (RTG) in geometry and topology at the University of California at Berkeley. The program will be led by six faculty members (Ian Agol, Denis Auroux, Michael Hutchings, John Lott, Peter Teichner, and Constantin Teleman), who will work in collaboration with other members of the Mathematics Department to build on the success of the previous RTG project by further enhancing the training of undergraduate students, graduate students, and postdoctoral fellows. The previous project incorporated a number of mechanisms for training enhancement, some of which worked better than others. The group will expand on the successful mechanisms and try follow-up innovations. With geometry and topology becoming ever more multifaceted and technical, it is difficult for students to acquire the tools they need for research. The activities of this research group will benefit trainees at all levels, beginning with a strong effort to recruit undergraduate students into research, continuing with seminars and hot topics courses to train graduate students in the latest techniques, and finally including mentoring to help postdoctoral fellows to launch their research careers. The mechanisms to provide such training will include an undergraduate research class during the school year taught by graduate students, a summer undergraduate research program run by graduate students under the guidance of senior faculty, undergraduate mentoring by postdoctoral fellows, a background seminar for graduate students and others, a geometry and topology colloquium, hot topics courses taught by senior faculty, summer graduate workshops taught by postdoctoral fellows, and an exchange program with the Max-Planck-Institute in Bonn. The project will involve approximately three postdoctoral associates, twelve graduate students per year, twelve undergraduates in each of the undergraduate research programs, and thirty participants in each of the summer graduate workshops. The proposed training activities will increase the number of US citizens and permanent residents entering and continuing in mathematics research, both directly and indirectly: directly via the recruiting and support of the trainees in the group, and indirectly via the establishment of models for research training that can be emulated elsewhere.