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. Jamming critical phase in linear soft spheres. Avalanches.
- Theory of the low temperature harmonic excitations of amorphous solids. Euclidean Random Matrices. Theory of localized soft excitations populating the quartic pseudogap at low frequencies in the DOS.
- 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. Persistent-SGD.
- 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.
Disordered mean field games
G. Parisi, P. Urbani, F. Zamponi. Theory of simple glasses. Cambridge University Press 2020.
IPhT Lectures on disordered and glassy systems