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.
Advanced PDE 1
-This is a first year course for PhD students for the local CDT. Syllabus and notes.
Real Analysis
- Covering theorems, maximal functions, Lebesgue's differentiation theorem, singular integrals, $L^p$ estimates, generalised functions.
Calculus of variations and differential geometry
- Theory of curves in $\mathbb R^2$ and $\mathbb R^3$. Hypersurfaces in $\mathbb R^3$. Notes.
Combinatorics and graph theory
- Basic counting laws, pigeon hole principle, recurrence relations, elements of graph theory.
Metric spaces
- Compactness, completeness, contraction and the fixed point theorem.
Linear Analysis
- Hilbert and Banach spaces, spectral theorem, Schwartz classes and distributions. Course page.
Mathematics for Engineers
- Basic ordinary differential equations and applications.