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小组，高级教员研究低维拓扑；准晶体、谱理论和数学物理；几何测度论；代数和复几何；以及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，包括本科生、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在几何以及相关的拓扑学和分析领域进行独立研究的人数。几何问题几乎在数学的每一个子领域都能刺激进步。由古希腊人发起的对二次曲线的研究在17世纪促进了坐标系和多项式代数的发展，导致了现代代数几何领域的发展。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，关于纽结和链环的几何问题导致了现代代数的许多进步。因此，几何例子提供了共同点，不同领域的专家可以交流想法和技术。莱斯的几何小组建立在这一共同点上，培训学生和博士后研究方法。