RTG: Algebraic Topology and Its Applications

近年来，代数拓扑学在数学内外得到了广泛的应用。例如，拓扑学为检测和描述复杂高维数据中的形状和结构提供了强大的新方法。该奖项支持俄亥俄州立大学代数拓扑及其应用研究培训小组。这项工作将在最近出现的高度协作和活跃的跨学科研究环境中进行，涉及数学系和计算机科学与工程系的研究人员。该项目的主要目标是为早期数学家和计算机科学家提供学习拓扑和相关领域的理论和应用方面的机会。接触这些主题将使学生和初级教师能够在一系列研究主题中流畅地移动，进入传统核心领域的研究社区，并在新的跨学科方向上工作。该奖项支持博士后研究人员、研究生和本科生研究拓扑相关领域，如几何群论、度量几何、计算几何和拓扑、结理论和随机拓扑。该奖项还支持新课程的开发，以及这些领域的工作组、研讨会和讲习班。项目的核心是强调在所有层次上进行指导。该项目还非常强调培养写作和沟通技巧，特别是博士后研究人员和参与研究小组的研究生。

Recently, algebraic topology has found a number of applications within mathematics and beyond. For example, topology provided powerful new methods for detecting and describing shape and structure in complex and high-dimensional data. This award supports the Research Training Group in Algebraic Topology and its Applications at Ohio State University. This work will be performed in a highly collaborative and active interdisciplinary research environment that has recently emerged, involving investigators from the Departments of Mathematics and Computer Science & Engineering. The main objective of the project is to provide early-stage mathematicians and computer scientists with opportunities to learn about both theoretical and applied aspects of topology and related fields. Exposure to these topics will allow students and junior faculty to move fluently across a range of research topics, to enter research communities in traditional core areas, and to work in new interdisciplinary directions.This award supports postdoctoral researchers, graduate students, and undergraduate researchers studying such topology-related fields as geometric group theory, metric geometry, computational geometry and topology, knot theory, and stochastic topology. The award also supports the development of new courses, as well as working groups, seminars, and workshops in these areas. At the heart of the project is an emphasis on mentoring at all levels. The program also places a strong emphasis on developing writing and communication skills, particularly for postdoctoral researchers and graduate students involved in the research group.