EMSW21-RTG: Geometry and Topology

EMSW21-RTG：几何和拓扑

• 批准号: 0943787
• 负责人: Tomasz Mrowka
• 金额: $ 159.23万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0943787&HistoricalAwards=false
• 关键词: EMSW21; RTG; Geometry; Topology

This project aims to promote research and training at the highest level in topology and geometry. The program spans a broad area of geometry and topology. The theory of minimal surfaces, their structure and more generally evolution of surfaces. Riemann geometry, in particular Einstein metrics and the space of metrics. Symplectic topology and relations to mirror symmetry, and low dimensional topology. Homotopy theory and its ever closer ties to number theory. Gauge theory and its applicationsto low dimensional topology. The MIT faculty involved in this program are leaders in these areas. The program, in addition to enhancing the research environment, will provide training and mentoring at all levels, postdocs, graduate students, and undergraduates. In addition the grant will allow the math department to support a undergraduate program for underrepresented minorities.Geometry and topology remains a major theme in present-day mathematics, and actively interacts with other areas ranging from number theory to physics. New ideas that have entered the subject recently have contributed to the solution of long-standing open problems in mathematics. Moreover the areas of mathematics supported by this program impact many areas of practical importance. Minimal surfaces and evolution of surfaces have historically been important for material sciences, chemistry and chemical engineering. Symplectic topology has had applications to understanding dynamical systems and lies at the heart of current work in high energy theoretic physics in the areas of string theory and mirror symmetry. Low dimensional topology has had applications to problems in biology in particular quantifying and understanding the knotted behavior of DNA as well as topological phases in matter.

该项目旨在促进拓扑和几何学最高水平的研究和培训。该程序跨越了几何和拓扑结构。最小表面的理论，它们的结构和表面的更普遍的演变。黎曼的几何形状，特别是爱因斯坦指标和指标空间。与镜像对称性和低维拓扑的符号拓扑和关系。 同质理论及其与数字理论的紧密联系。仪表理论及其应用范围低维拓扑。 参与该计划的麻省理工学院教师是这些领域的领导者。该计划除了增强研究环境外，还将在各个级别，博士后，研究生和本科生提供培训和指导。此外，该赠款将允许数学部支持一项针对代表性不足的少数群体的本科计划。几何和拓扑仍然是当今数学的主要主题，并与从数字理论到物理学的其他领域进行积极互动。最近进入该主题的新想法有助于解决数学长期开放问题的方法。此外，该计划支持的数学领域影响了许多实际重要的领域。历史上对材料科学，化学和化学工程的最小表面和表面的演变至关重要。 符合性拓扑已经在理解动力学系统的核心方面有应用，在弦理论和镜像对称性领域中，当前工作的核心是高能理论物理学的核心。低维拓扑已应用于生物学问题，特别是量化和理解了物质中DNA的打结行为以及拓扑阶段。