Pierfrancesco Urbani

CNRS Researcher

Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France

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I am a statistical physicist working on disordered and glassy systems and on their applications to optimization, inference and machine learning problems.

My activity has focused on the construction of a theory of the glass phase starting from the soluble yet non-perturbative limit of infinite dimensions. The main result is that it has allowed to obtain a new phase diagram of glasses at low temperature which has shown the emergence of the so-called Gardner phase in which amorphous solids are marginally stable against external perturbations. This phase is the potential missing ingredient to unify the physics of anomalies of low temperature glasses and a large part of my recent activity has gone in this direction. The consequences of this discovery are already well established for colloidal-like glasses where we have shown that the Gardner phase is crucial for the computation of the critical exponent of the jamming transition and jamming-critical systems. My activity now focuses on the understanding of how marginal stability associated to the Gardner phase gives rise to non-linear excitations in amorphous solids. These excitations are typically postulated in phenomenological approaches to the rheology of amorphous solids. My main goal is to understand their dynamical generation from microscopic interactions and to uncover their collective nature and statistical properties.

Recently I also got more interested in the application of glass physics ideas to high dimensional optimization problems. Here I mainly focused on the study of minimization algorithms and their properties in a quite extended set of problems, going from high-dimensional inference problems, to learning in simple neural networks.

Main research activities and results

Solution of structural glass models in infinite dimension:

Constraint satisfaction and optimization problems

High-dimensional statistical inference and machine learning

Field theory and renormalization

Disordered high dimensional optimal control


G. Parisi, P. Urbani, F. Zamponi. Theory of simple glasses. Cambridge University Press 2020.

Google Scholars , Arxiv



IPhT Lectures on disordered and glassy systems (video)

Les Houches Lectures on dynamics in high dimension (2020) (lecture 1, lecture 2, lecture 3)





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