RTG: Geometry and topology at the University of Chicago

该奖项为芝加哥大学几何和拓扑学研究培训小组的参与者提供支持。该项目将由六名教员(丹尼·卡莱加里、亚历克斯·埃斯金、本森·法布、J·彼得·梅、Shmuel Weinberger和Anne M.Wilkinson)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，在该系在学年定向阅读计划和本科生暑期研究经验计划方面取得的成功的基础上再接再厉。研究生和博士后将参与博士后教授的专题课程，并支持本科生以研究为导向的暑期项目。为研究生和博士后举办的较短、身临其境的暑期研讨会将建立在中西部拓扑学研讨会和相关会议的长期传统基础上，这些会议定期将整个五大湖州的研究人员聚集在一起。本学年的小组活动包括一个主题广泛的几何识字课程和一个拓扑学专题讨论会。这个研究培训小组的目的是实现几十年来分离的领域的更大程度的整合，并使参与者接触到比传统更广泛的潜在应用。研究培训将以广泛的研究主题为基础，包括动力系统和遍历理论，几何群论及其周围的各种主题，算术网格中刚性的显著失效，同调稳定性现象，以及代数拓扑中的各种主题，从等变稳定同伦理论到应用代数拓扑和数据分析。

This award provides support for participants in the research training group in geometry and topology at the University of Chicago. The program will be led by six faculty members (Danny Calegari, Alex Eskin, Benson Farb, J. Peter May, Shmuel Weinberger, and Anne M. Wilkinson) who will work in collaboration with other members of the Department of Mathematics to build on the department's successes in the academic year Directed Reading Program and summer Research Experience for Undergraduates program by further enhancing the training of undergraduate students, graduate students, and postdoctoral fellows. Graduate students and postdocs will be involved in topics courses taught by postdocs and in the support of research-oriented summer programs for undergraduates. Shorter, immersive summer workshops for graduate students and postdocs will build on the longstanding tradition of the Midwest Topology Seminar and related conferences that regularly bring together researchers throughout the Great Lakes states. Group activities for the academic year include a geometric literacy course that ranges widely in topics, and a topology proseminar.This research training group aims to achieve a greater integration of fields that have grown apart over the decades and to expose participants to a broader range of potential applications than has been traditional. Research training will be anchored by research topics ranging broadly through dynamical systems and ergodic theory, a variety of topics in and around geometric group theory, the striking failure of rigidity in arithmetic lattices, homological stability phenomena, and various topics in algebraic topology, from equivariant stable homotopy theory through applied algebraic topology and data analysis.