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...
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