Kondo effect and the renormalization group
Quantum physics in one dimension, hydrodynamical approach, orthogonality catastrophe, bosonization, Jordan-Wigner transformation

Renormalization group analysis of the Sine-Gordon model, semiclassical interpretation of strong coupling theory

Quantum Magnetism: Jordan-Wigner transformation, spin chains, Lieb-Shultz- Mattis theorem, the Haldane gap

Symmetry breaking, mean field theory, long range order, effective theory and Goldstone modes

Superfluidity versus superconductivity, Anderson-Higgs mechanism

Low dimensional systems, Mermin-Wagner theorem, the xy model, Kosterlitz-Thouless transition

Topological phases and Quantum Hall effect: Topological field theory, Chern-Simons theory, Berry phase,topological band insulators, topological superconductors, Majorana fermions