IntroductionThis course will use a material written by J.Carlström. It can be downloaded byhttps://bimsa.net/doc/notes/logic2008.pdf SyllabusDay 1 Introduction• History and purpose of logic.• Boolean algebras.Inductively defined sets (Ch. 3 of Carlström)• Motivation: What is formal syntax? What are formulas?• The natural numbers; recursion and induction principles• General inductively defi...
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, ...