Elastic objects, models and physical examples. Coupling to substrates: quenched disorder, models, examples, universality classes. What do we learn from experiments (superconductors, magnetic domains, wetting, etc) ? Physics of pinning: Larkin model, with and without replica, stability; beyond Larkin (Flory); depinning transition (phenomenology); glassy dynamics and creep motion; driven dynamics: Edwards Wilkinson and Kardar Parisi Zhang equations.
Random energy landscapes and decaying Burgers turbulence. Sinai model, real space Renormalization Group (RG) of Brownian Landscape, shocks and droplets, zero temperature fixed point, thermally activated motion. Log-correlated landscapes, freezing transitions, Coulomb gas and directed polymer on Cayley tree: statics and dynamics. Toy models for depinning, avalanches and creep.
What is needed in field theory, RG and exact RG: a short review.
Static Functional RG: perturbation theory, dimensional reduction, definition of renormalized disorder, effective action, one loop Functional RG at zero temperature, applications.
Dynamic Functional RG: diagrammatics and connection to statics, differences with statics, two loop (sketch), depinning transition, moving states.
Shocks and avalanches. Including temperature: Cardy Ostlund model, marginal glass, back to Coulomb gas, mesoscopic fluctuations, thermal boundary layer: droplets and creep. Large N: Gaussian Variational Method, Replica Symmetry Breaking and mean-field connection to Functional RG. Exotic disorders: correlated disorder, pinning of quantum systems. Opening on other problems: random fields, gauge glasses, RFIM, reaction diffusion.