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 analysis

Reference：

C.D. Sogge, Hangzhou lectures on eigenfunctions of the Laplacian, volume 188 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2014.

C.D. Sogge, Fourier integrals in classical analysis, volume 210 of Cambridge Tracts in Mathematics.Cambridge University Press, Cambridge, second edition, 2017.