Triangulations in dimension three: algorithms and geometric structures

第三维度的三角测量：算法和几何结构

• 批准号: DP1095760
• 负责人: Prof Joachim Rubinstein
• 金额: $ 23.99万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2010
• 资助国家: 澳大利亚
• 起止时间: 2010-01-27 至 2013-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP1095760
• 关键词: Triangulations; dimension; three; algorithms; geometric

Perelman recently won a Fields medal for the solution of the geometrisation and Poincare conjectures on three-dimensional spaces, using a very deep heat flow method to find optimal geometries on these spaces. The project will develop a new constructive approach to building these optimal geometric structures. This will lead to effective algorithmic methods to distinguish three-dimensional spaces, with applications to the study of knots and links (for example, knotted DNA molecules) and to mathematical physics. The project will also provide new techniques to study important problems in the classification of three-dimensional spaces, such as the virtual Haken conjecture.

佩雷尔曼最近赢得了菲尔兹奖的解决方案的geometrisation和庞加莱几何的三维空间，使用一个非常深的热流方法，以找到最佳的几何形状对这些空间。该项目将开发一种新的建设性方法来构建这些最佳几何结构。 这将导致有效的算法方法来区分三维空间，并应用于研究结和链接（例如，打结的DNA分子）和数学物理。该项目还将提供新的技术来研究三维空间分类中的重要问题，如虚拟哈肯猜想。