Statistical physics of complex systems: glasses, spin glasses, continuous constraint satisfaction problems, high-dimensional inference and neural networks

The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is the subject of the first chapter where I discuss a new model, the KHGPS model, which allows to make some progress. In the second chapter I review a second research line that concerns the study of the rigidity/jamming transitions in particle system models and their relation to constraint satisfaction and optimization problems in high dimension. Finally in the last chapter I review my activity on the problem of the dynamics of learning algorithms in high-dimensional inference and supervised learning problems.