William Rowan Hamilton Geometry and Topology Workshop; September 2009, Dublin, Ireland

该奖项支持美国演讲者，并邀请美国青年研究人员参加2009年9月17日至19日在爱尔兰都柏林汉密尔顿数学研究所举行的第五届威廉·罗文·汉密尔顿几何和拓扑研讨会，这是一个为期3天的计算和算法几何指导研讨会。研讨会的参与者包括来自低维拓扑、几何群论和双曲几何领域的主要研究人员、初级研究人员和研究生，他们对几何和拓扑中的计算和算法问题有特殊的兴趣。具体的主题包括小体积双曲3-流形的结构和随机流形的理论。在小体积双曲三流形理论中，Gabai-Meyerhoff-Milley引入了Mom技术来研究小体积双曲流形。在会议期间，我们将考虑这些技术在提供小体积双曲流形的清晰图像方面能走多远。在几何群论中，工作坊将考虑曲率和组合在决策问题中的一般作用。研究低维拓扑、几何群论和双曲几何的数学家关注对称性的本质。例子包括雪花的对称性，建筑中的雕花图案，墙纸和瓷砖图案，以及化学中晶体或晶格结构的对称性。计算机已经成为这项研究中不可或缺的工具，既可以证明新的结果，也可以通过实验和计算激发新的方向。该奖项将使来自美国的主要研究人员、研究生和初级研究人员能够与来自世界各地的研究人员聚集在一起，以结合方法和技术来进一步开展这项研究。这项活动将有助于下一代研究人员的研究项目，并将加深我们对对称本质的理解。这项活动支持一个正在进行的国际研讨会，致力于在美国数学界和欧洲新兴的数学研究所（汉密尔顿数学研究所）之间建立联系。

The award supports US speakers and invited US junior researchers attending the fifth William Rowan Hamilton Geometry and Topology Workshop, a 3-day, directed workshop on Computational and Algorithmic Geometry to be held at the Hamilton Mathematics Institute in Dublin, Ireland in September 17-19, 2009. Participants at the workshop include leading researchers, junior researchers and graduate students from the fields of low dimensional topology, geometric group theory, and hyperbolic geometry who have a special interest in computational and algorithmic problems in geometry and topology. Specific topics include the structure of low-volume hyperbolic 3- manifolds and the theory of random manifolds. In low-volume hyperbolic 3-manifold theory Gabai-Meyerhoff-Milley introduced the Mom technology to study low volume hyperbolic manifolds. During the conference we will consider how far the techniques can be pushed to provide a clear picture of low volume hyperbolic manifolds. In geometric group theory, the workshop will consider the general role of curvature and combinatorics in decision problems. Mathematicians who study low dimensional topology, geometric group theory, and hyperbolic geometry are concerned about the nature of symmetry. Examples include the symmetries of a snowflake, frieze patterns in architecture, wallpaper and tiling patterns, and symmetries of crystal or lattice structures in chemistry. Computers have become an integral tool in this study, both for proving new results as well as motivating new directions through experiment and calculation. This award will enable leading researchers, graduate students and junior researchers from the US to gather together with researchers from around the world in order to combine methods and techniques to further this research. This activity will help focus the research programs of the next generation of researchers, and will deepen our understanding of the nature of symmetry. This activity supports an ongoing international workshop dedicated to forging bonds between the US mathematics community and an emerging mathematics institute (the Hamilton Mathematics Institute) in the European community.