Main research activities and results
Solution of structural glass models in infinite dimension:
- Gardner transition in structural glasses: mean field theory and RG analysis.
- Theory of the Jamming transition: computation of the critical exponents and characterization of marginal stability; jamming of non-spherical particles, upper critical dimension and hyperuniformity.
- Theory of the low temperature harmonic excitations of amorphous solids.
- Microscopic theory of rheology of amorphous solids: yielding as a critical spinodal with emerging RFIM criticality, shear-jamming of stable hard sphere glasses, two-step yielding, stability map of glasses, breakdown of elasticity at low temperatures.
- Dynamical Criticality: computation of the dynamical critical exponents at the MCT transition as well as at the Gardner point.
- Quasi-equilibrium approach to the dynamics of structural glasses.
Constraint satisfaction and optimization problems
- Jamming in multilayer neural networks.
- Emergence of isostatic marginally stable critical phases both in infinite and finite dimensional optimization problems. Theory of the corresponding non-linear excitations.
- Dynamical mean field theory for gradient-based optimization.
High-dimensional statistical inference and machine learning
- Glassy nature of the hard phase of inference problems
- Emergence of a generic gap between gradient based algorithms and message passing ones.
- Analysis of gradient descent dynamics in high-dimensional inference problems.
- Dynamical mean field theory for stochastic gradient descent.
- Replica-symmetry-breaking implementation of Approximate Message Passing algorithms.
Field theory and renormalization
- Field theory for the glass transition. Dynamical heterogeneities.
- Non-perturbative renormalization group approach to instantons.
G. Parisi, P. Urbani, F. Zamponi. Theory of simple glasses. Cambridge University Press 2020.
IPhT Lectures on disordered and glassy systems