Francesco Zamponi, ENS Paris, France

Theory of the glass and jamming transitions in infinite dimensions (10.5h)

1. Atomic liquids in infinite dimensions, thermodynamics: Basic observables, the virial expansion, virial expansion in large dimensions, hard spheres and other potentials.

2. Atomic liquids in infinite dimensions, equilibrium liquid dynamics: Models of equilibrium dynamics, basic observables, self-consistent dynamical mean field equations, properties of the liquid phase.

3. Atomic liquids in infinite dimensions, Dynamical arrest: Dynamical glass transition, calculation of the plateau of dynamical correlations, critical properties of the dynamical transition.

4. State following: Replica symmetric results: the Franz-Parisi construction, calculation of the Franz-Parisi free energy in infinite dimensions, replica symmetry, phase diagram of thermal glasses, phase diagram of hard sphere glasses: glass vs jamming transitions.

5. Complexity: Replica symmetric results, equilibrium complexity, out-of-equilibrium complexity, the Monasson method, phase diagram, connection with the Edwards ensemble for hard spheres, protocol dependence of the jamming transition.

6. Elements of replica symmetry breaking: Hierarchical free energy landscapes, an introduction to replica symmetry breaking, equations for the Gardner transition, replica symmetry breaking phase diagram, critical exponents for the jamming transition.

7. Discussion and closing remarks.