Geometric Invariants and Metric Degenerations

小行星9704296 该项目涉及光谱几何和几何不变量领域的各种问题。该研究员是研究流形与圆锥奇点，以期对定义和理解某些几何不变量，如分析扭转在一个更一般的设置;研究谱几何退化度量下的各种过程，包括绝热极限，黎曼崩溃;研究几何不变量和他们的行为下手术。 光谱几何是一个经常使用分析技术来研究几何对象的领域。该项目特别涉及通过热方程技术定义某些几何不变量-热方程是更着名的偏微分方程之一，描述热流现象，并且对方程有很多了解。

9704296 Dai This project deals with a variety of problems in the area of spectral geometry and geometric invariants. The investigator is to study manifolds with conical singularity with a view towards defining and understanding certain geometric invariants such as analytic torsion in a more general setting; to study the spectral geometry of degenerating metrics under various processes including the adiabatic limit, and Riemannian collapsing; to study geometric invariants and their behavior under surgery. Spectral geometry is an area where often analytic techniques are used to study geometric objects. This project in particular deals with defining certain geometric invariants via heat equation techniques - the heat equation is among the more well-known partial differential equations, describing the heat flow phenomenon, and much is known about the equation.