RTG: Geometry and Topology

该奖项为加州大学伯克利分校几何和拓扑学研究培训小组(RTG)的参与者提供持续支持。该计划将由六名教员(Ian Agol、Denis Auroux、Michael Hutchings、John Lott、Peter Teichner和Constantin Teleman)领导，他们将与数学系其他成员合作，通过进一步加强对本科生、研究生和博士后研究员的培训，在先前RTG项目的成功基础上再接再厉。前一个项目纳入了一些加强培训的机制，其中一些机制的效果比另一些机制要好。该小组将对成功的机制进行扩展，并尝试后续创新。随着几何学和拓扑学变得越来越多面性和技术性，学生很难获得他们研究所需的工具。这个研究小组的活动将使各级受训人员受益，从大力招收本科生进入研究，继续通过研讨会和热门话题课程培训研究生最新技术，最后包括辅导，帮助博士后研究员开始他们的研究生涯。提供这种培训的机制将包括在学年期间由研究生授课的本科生研究课程、由研究生在高级教师指导下举办的夏季本科生研究项目、由博士后研究员指导的本科生本科生指导、为研究生和其他人举办的背景研讨会、几何和拓扑学座谈会、高级教师讲授的热门话题课程、博士后研究员授课的暑期研究生研讨会，以及与波恩的马克斯·普朗克研究所的交流项目。该项目将涉及大约3名博士后助理，每年12名研究生，每个本科生研究项目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进入和继续从事数学研究的美国公民和永久居民的数量：直接通过招募和支持小组中的受训者，间接通过建立可在其他地方效仿的研究培训模式。

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.