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

威廉·罗文·汉密尔顿几何与拓扑研讨会；

• 批准号: 0937256
• 负责人: Martin Bridgeman
• 金额: $ 1.8万
• 依托单位: Boston College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0937256&HistoricalAwards=false
• 关键词: William; Rowan; Hamilton; Geometry; Topology

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.

该奖项支持参加第五届William Rowan哈密尔顿几何和拓扑研讨会的美国演讲者和受邀的美国初级研究人员，这是一个为期3天的计算和算法几何指导研讨会，将于2009年9月17-19日在爱尔兰都柏林的汉密尔顿数学研究所举行。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顶尖研究人员、初级研究人员和研究生，他们对几何和拓扑学中的计算和算法问题特别感兴趣。具体主题包括低体积双曲3-流形的结构和随机流形理论。在低体积双曲3-流形理论中，Gabai-Meyerhoff-Milley引入了MoM技术来研究低体积双曲流形。在会议期间，我们将考虑这些技术可以推进到什么程度，以提供低容量双曲线流形的清晰图景。在几何群论中，工作坊将考虑曲率和组合学在决策问题中的一般作用。研究低维拓扑学、几何群论和双曲几何的数学家关心对称性的本质。例如雪花的对称性，建筑中的浮雕图案，墙纸和瓷砖图案，以及化学中晶体或晶格结构的对称性。在这项研究中，计算机已经成为一个不可或缺的工具，既可以证明新的结果，也可以通过实验和计算来激励新的方向。该奖项将使来自美国的顶尖研究人员、研究生和初级研究人员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促进这项研究。这项活动将有助于聚焦下一代研究人员的研究计划，并将加深我们对对称性本质的理解。这项活动支持正在进行的一个国际研讨会，该研讨会致力于在美国数学界和欧洲共同体的一个新兴数学研究所(汉密尔顿数学研究所)之间建立联系。