Abstract: | In this series of lectures we will introduce the quantitative homogenization theory of second-order linear elliptic equations and systems in divergence form with almost-periodic coefficients. We will start with the definition and properties of almost-periodic functions, and present the classical qualitative homogenization theory. The main body of the lectures will deal with the key issues in the quantitative theory: estimates of approximate correctors, convergence rates, uniform regularity estimates (H"older, Lipschitz, W^{1, p}). The lectures are designed for advanced graduate students as well as junior researchers in the general areas of analysis and PDEs. We assume that the audience is familiar with the basic material usually covered in the first-year graduate courses on real analysis, functional analysis, and linear elliptic PDEs. |