# Aram KarakhanyanLecturer in Mathematics The University of Edinburgh

Second order elliptic PDEs
-De Giorgi's theorem on $C^\alpha$ regularity, Harnack principles, Krylov-Safonov estimate. Notes.
- Covering theorems, maximal functions, Lebesgue's differentiation theorem, singular integrals, $L^p$ estimates, generalised functions.
- Theory of curves in $\mathbb R^2$ and $\mathbb R^3$. Hypersurfaces in $\mathbb R^3$. Notes.