Description: We will introduce the problems and methods on eigenfunctions of the Laplacian.Contents: Review of the Laplacian and the d'Alembertian, the Hadamard parametrix, the sharp Weyl formula, stationary phase and microlocal analysis, improved spectral asymptotics and periodic geodesics, classical and quantum ergodicity.Prerequisite:Real analysis, functional analysisReference:C.D. Sogge, ...
Record: YesLevel: GraduateLanguage: ChinesePrerequisitebasic knowledge of measure theory, stochastic process, functional analysis and topologyAbstractWe will introduce basis knowledge of ergodic theory, and its relationship with dynamical systems. This course includes topics on measure-preserving transformation, entropy and topological entropy.Reference1. Peter Walters: An introduction to erg...