Here are the titles and brief description of the lectures:
1. A brief and quick introduction to two-scale expansions method (Harsha)
This lecture will cover the following topics: two-scale asymptotic expansion, cell problem, homogenized coefficients.
2. Elliptic regularity in L^2 (Vivek)
This lecture will cover the following topics: Caccioppoli's inequality, interior estimates via difference quotients.
3. Tartar's method of oscillatory of test functions (Muthukumar)
This lecture describes the oscillatory test function method for passing to the limit in the periodic elliptic homogenization problem.
4. Elliptic Schauder estimates (Vivek)
These lectures will cover the following topics: Companato characterization of Holder spaces, Schauder estimates.
5. Elliptic regularity in L^p (Chandan)
These lectures will cover the following topics: Hausdorff-Young inequality, nontangential Maximal function, Calderon-Zygmund argument, Hardy-Littlewood-Sobolev inequality.
6. Homogenization in periodic perforated domains (Vanninathan)
These lectures will cover the following topics: Homogenization of Stokes equation in periodically perforated domains, Strange term coming from nowhere.
7. Rates of convergence for Stokes operator (Hari)
This lecture will cover the following topic: Convergence rates for homogenization of Stokes equation in perforated domains.
8. Introduction to boundary layers and critical size analysis (Aiyappan)
These lectures will cover the following topics: Boundary layers in periodic homogenization, critical size analysis in the homogenization of Stokes equation in periodically perforated domains.
9. Quantitative rates of convergence in H^1, L^2 and L^p (Kshitij)
These lectures will cover the following topics: properties of a smoothing operator, quantitative rates for periodic homogenization of elliptic systems.
10. Quantitative theory of periodic homogenization for parabolic equations (Tuhin)
These lectures will cover the following topics: convergence rates and uniform regularity estimates for homogenization of parabolic equations.
11. Homogenization of non-divergence form elliptic operators (Harsha)
These lectures will cover the following topics: homogenization of non-divergence form elliptic systems, Connection to coefficients with divergence free columns.
12. Quantitative regularity results in periodic homogenization and related topics (Christophe)
These lectures will cover the following topics: large-scale regularity via compactness, large-scale regularity via quantitative estimates (Schauder approach), recent results on the boundary layer analysis in periodic homogenization, a brief intro to the idea of renormalization.
13. Homogenization of High-contrast optimal control problem in oscillatory domain via unfolding method (Nandakumaran)