RTG: Geometry and Topology

该奖项为加州大学伯克利分校几何和拓扑研究培训小组 (RTG) 的参与者提供持续的支持。 该项目将由六名教员（Ian Agol、Denis Auroux、Michael Hutchings、John Lott、Peter Teichner 和 Constantin Teleman）领导，他们将与数学系的其他成员合作，在之前 RTG 项目成功的基础上进一步加强对本科生、研究生和博士后的培训。之前的项目纳入了许多增强培训的机制，其中一些机制比其他机制效果更好。集团将在成功机制的基础上进行拓展，并尝试后续创新。随着几何和拓扑变得越来越多方面和技术性，学生很难获得研究所需的工具。该研究小组的活动将使各级学员受益，首先是大力招募本科生进行研究，然后是研讨会和热点课程，以培训研究生最新的技术，最后包括指导，帮助博士后开展他们的研究生涯。提供此类培训的机制将包括研究生在学年开设的本科生研究班、研究生在高级教师指导下开展的暑期本科生研究项目、博士后研究员的本科生指导、研究生和其他人的背景研讨会、几何和拓扑研讨会、高级教师教授的热点课程、博士后教授的夏季研究生研讨会以及与波恩马克斯普朗克研究所的交流项目。该项目将涉及大约三名博士后、每年十二名研究生、每个本科研究项目的十二名本科生以及每个夏季研究生研讨会的三十名参与者。拟议的培训活动将直接和间接地增加进入和继续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学员，间接通过建立可在其他地方效仿的研究培训模型。

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.