EMSW21-RTG: Graduate Education in Geometry and Topology at the University of Chicago

摘要奖：DMS-0354270首席研究员：Kevin D.Corlett这个项目将支持芝加哥大学几何/拓扑学小组的活动，这些活动对研究生的培养产生了影响。这一群体目前由6名高级教员、13名初级教员和约30名研究生组成。该小组成员的研究兴趣涵盖了广泛的几何和拓扑学主题，包括复微分几何、刚性和局部对称空间、遍历理论与离散群和数论的联系、几何群论、三维流形拓扑、TeichMuller理论、高维流形的几何拓扑、黎曼度量的模空间、复动力学、辛拓扑和同伦理论。该小组的活动包括几何/拓扑学和代数拓扑学的活跃研究研讨会，几个学生研讨会和一个访客计划，所有这些都与研究生的教育直接相关。这些活动与本系研究生课程的总体结构相结合，为学生在从事自己的具体研究项目的同时接触到广泛的当前研究提供了理想的条件。几何和拓扑学是数学的基础部分，目前正在经历快速发展，许多新的想法和研究路线正在被追寻。这些发展中的许多都是学科本身的，而另一些则至少部分是由于与物理和计算机科学等领域的接触而产生的。身为一名经历这种变化的学生尤其令人兴奋，但同时也是一种挑战，在环境快速变化的情况下如何定位自己。该项目将提高芝加哥大学博士生在这些领域学习和研究的能力，从而帮助培养下一代几何和拓扑学研究人员。除了为研究生提供研究方面的直接支持外，该项目还将为毕业生参加会议和吸引访问者到大学进行研讨会演讲和合作提供支持。所有这些都是为了让研究生尽可能有效地接触到研究的第一线。

AbstractAward: DMS-0354270Principal Investigator: Kevin D. CorletteThis project will support activities of the geometry/topologygroup at the University of Chicago which have an impact on thetraining of graduate students. This group currently consists ofsix senior faculty, thirteen junior faculty and about thirtygraduate students. The research interests of members of thegroup span a wide array of topics in geometry and topology,including complex differential geometry, rigidity and locallysymmetric spaces, connections of ergodic theory with discretegroups and number theory, geometric group theory, 3-manifoldtopology, Teichmuller theory, geometric topology ofhigh-dimensional manifolds, the moduli space of Riemannianmetrics, complex dynamics, symplectic topology and homotopytheory. The activities of the group include active researchseminars in geometry/topology and algebraic topology, severalstudent seminars and a visitors program, all of which aredirectly relevant to the education of graduate students. Theseactivities, in combination with the general structure of thegraduate program in the department, provide ideal conditions forstudents to gain exposure to a broad range of current researchwhile pursuing their own specific research projects.Geometry and topology are fundamental parts of mathematics whichare currently experiencing rapid development, with many new ideasand lines of investigation being pursued. Many of thesedevelopments are internal to the subject, while others arise, atleast in part, from contact with fields such as physics andcomputer science. It is particularly exciting to be a student ina field undergoing this kind of change, but it is at the sametime a challenge to orient oneself when the landscape is rapidlychanging. This project will enhance the ability of doctoralstudents at the University of Chicago to learn about and doresearch in these areas, thus helping to train the nextgeneration of researchers in geometry and topology. In additionto providing direct support for graduate students as they doresearch, the project will also provide support for graduatestudents to travel to conferences and the bring visitors to theUniversity for seminar talks and collaboration. All of this isintended to expose graduate students to the frontlines ofresearch as effectively as possible.