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的几何组，具有低维拓扑的高级教职员工；准晶体，光谱理论和数学物理学；几何衡量理论；代数和复杂的几何形状；以及Teichmueller理论和最小表面。 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从几何学领域进行独立研究的学生和博士后的数量，以及拓扑和分析的相关领域。几乎刺激了几乎每个数学子领域的进步。 古希腊人发起的圆锥切片的研究刺激了17世纪的坐标系统和多项式代数的发展，导致了代数几何的现代领域。 寻找曲线和表面最小化物理系统能量的愿望激发了微积分的发展。 最近，有关结和链接的几何问题导致了现代代数的许多进步。 因此，几何示例提供了共同的基础，不同领域的专家可以交换思想和技术。 稻米的几何组建立在这个共同的基础上，以培训学生和博士后研究员的数学研究方法。