Geometry and Topology Down Under

澳大利亚的几何和拓扑

• 批准号: 1110730
• 负责人: William Jaco
• 金额: $ 3.5万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1110730&HistoricalAwards=false
• 关键词: Geometry; Topology; Down; Under

A Workshop and Conference is being held at the University of Melbourne, Australia, to bring together active, leading, international experts and emerging researchers to report on recent results and explore future directions in the field of Geometry and Topology. Particular emphasis will be placed on one of its most active branches, the study of 3-manifolds. Geometric structures on 3-manifolds are known to exist by Perelman's work on the Ricci flow, but relatively little is known about the interplay between analysis and geometry, and how to construct geometric structures directly. The Workshop will be targeted at early career researchers and will feature short courses covering a broad range of materials and techniques being used at the frontier of research in dynamical and probabilistic methods in geometric group theory, invariants of hyperbolic 3-manifolds, and new methods in distinguishing knots and links. The Conference will highlight ongoing research focused on finding direct connections between analysis, geometry, and topology of 3-manifolds. This project will enable Early Research Career mathematicians from the United States to attend a Workshop and Conference at the University of Melbourne, Australia, on recent results and new directions in the geometry and topology of 3-manifolds. This is one of the most active and rapidly changing areas of mathematical research. Participation will give these young researchers access to short courses on new results and techniques for future research and bring them together with leading international experts in the area. The Workshop and Conference will have broad appeal to group theorists, analysts, differential geometers, and low-dimensional topologists. It will bring about interaction between emerging researchers and experts and expose the potential for future collaborations.

正在澳大利亚墨尔本大学举行一次讲习班和会议，将活跃的、领先的国际专家和新兴研究人员聚集在一起，报告几何和拓扑学领域的最新成果并探讨未来的方向。特别强调将放在其最活跃的分支之一，3流形的研究。 3-流形上的几何结构通过佩雷尔曼关于里奇流的工作而被发现，但对于分析和几何之间的相互作用以及如何直接构造几何结构知之甚少。该研讨会将针对早期的职业研究人员，并将提供短期课程，涵盖广泛的材料和技术，用于几何群论中的动力学和概率方法研究的前沿，双曲3-流形的不变量，以及区分结和链接的新方法。会议将突出正在进行的研究，重点是寻找分析，几何和3-流形拓扑之间的直接联系。该项目将使来自美国的早期研究职业数学家能够参加在澳大利亚墨尔本大学举行的研讨会和会议，讨论三维流形几何和拓扑学的最新成果和新方向。 这是数学研究中最活跃和变化最快的领域之一。参与将使这些年轻的研究人员有机会参加关于未来研究新成果和技术的短期课程，并使他们与该领域的主要国际专家聚集在一起。研讨会和会议将有广泛的吸引力组理论家，分析师，微分geometers，和低维拓扑学家。它将带来新兴研究人员和专家之间的互动，并揭示未来合作的潜力。