RTG: Analysis, Geometry, and Topology at Rice University

RTG：莱斯大学的分析、几何和拓扑

• 批准号: 1148609
• 负责人: David Damanik
• 金额: $ 162.77万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1148609&HistoricalAwards=false
• 关键词: RTG; Analysis; Geometry; Topology; Rice

Rice University has a dynamic geometry group, with senior faculty in low- dimensional topology; quasi-crystals, spectral theory, and mathematical physics; geometric measure theory; algebraic and complex geometry; and Teichmueller theory and minimal surfaces. This project will support a Research Training Group led by these faculty, involving undergraduate students, graduate students, and postdoctoral fellows. Our main objective is to increase the number of students and postdocs pursuing independent research in geometry, as well as related areas of topology and analysis.Geometric problems stimulate progress across almost every subfield of mathematics. The study of conic sections initiated by the ancient Greeks spurred the development of coordinate systems and polynomial algebra in the 17th century, leading to the modern field of algebraic geometry. The desire to find curves and surfaces minimizing the energy of physical systems motivated the development of calculus. More recently, geometric questions about knots and links have led to numerous advances in modern algebra. Thus geometric examples offer common ground where specialists in different areas can exchange ideas and techniques. The Geometry Group at Rice builds on this common ground to train students and postdoctoral fellows in the methods of mathematical research.

莱斯大学有一个动态几何组，高级教师在低维拓扑;准晶体，光谱理论，数学物理;几何测量理论;代数和复杂的几何;和Teichmueller理论和极小曲面。 该项目将支持由这些教师领导的研究培训小组，涉及本科生，研究生和博士后研究员。 我们的主要目标是增加学生和博士后追求独立研究的几何，以及拓扑和分析的相关领域的数量。几何问题刺激几乎每一个数学领域的进步。 由古希腊人发起的圆锥曲线的研究促进了世纪坐标系和多项式代数的发展，导致了现代代数几何领域。 寻找使物理系统的能量最小化的曲线和曲面的愿望推动了微积分的发展。 最近，关于结和环的几何问题导致了现代代数的许多进步。 因此，几何的例子提供了共同的基础，不同领域的专家可以交流思想和技术。 在赖斯几何组建立在这个共同点，培养学生和博士后研究员在数学研究的方法。