Introduction to spectral geometry
授课人：王作勤 教授 （中国科学技术大学）
内容简介：Spectral geometry is the branch of mathematics that studies the relation between the eigenvalues of (usually Laplace-related) geometric operators and the background geometry. In this short course, I will give a brief introduction to this area: brackgrounds, some classical results as well as some open problems. I will start with some basic facts and examples, and then I will focus on the following fundamental problems in spectral geometry: the behavior of small eigenvalues (e.g. various isoperimetric inequalities for eigenvalues), and the behavior of large eigenvalues (Weyl laws etc).