Geometry and Topology Down Under

一个研讨会和会议正在澳大利亚墨尔本大学举行，汇集了活跃的，领先的，国际专家和新兴的研究人员，报告最近的成果和探索几何和拓扑领域的未来方向。特别的重点将放在其最活跃的分支之一，3流形的研究。3-流形上的几何结构是由Perelman关于Ricci流的工作所知道的，但相对而言，人们对分析与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。工作坊将以早期职业研究人员为目标，并将以短期课程为特色，涵盖广泛的材料和技术，用于几何群论的动态和概率方法的研究前沿，双曲3流形的不变量，以及区分结和连接的新方法。会议将重点关注正在进行的研究，重点是寻找3流形的分析、几何和拓扑之间的直接联系。该项目将使来自美国的早期研究生涯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3流形几何和拓扑的最新成果和新方向。这是数学研究中最活跃、变化最迅速的领域之一。参与将使这些年轻的研究人员有机会参加有关未来研究的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会面。研讨会和会议将广泛吸引群论学家、分析学家、微分几何学者和低维拓扑学家。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。

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.