## 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.