RTG: Analysis, Geometry, and Topology at Rice University

莱斯大学有一个动态几何小组，在低维拓扑方面有资深的教师；准晶体、光谱理论和数学物理；几何测量理论；代数和复几何；Teichmueller理论和最小曲面。该项目将支持一个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。我们的主要目标是增加在几何以及拓扑和分析相关领域进行独立研究的学生和博士后的数量。几何问题几乎刺激了数学各个分支领域的进步。古希腊人对二次曲线的研究刺激了17世纪坐标系统和多项式代数的发展，导致了现代代数几何领域的发展。寻找能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，关于结点和连杆的几何问题导致了现代代数的许多进步。因此，几何例子为不同领域的专家提供了交流思想和技术的共同基础。莱斯大学的几何小组以这一共同基础为基础，培养数学研究方法方面的学生和博士后。

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.