Some problems on mean-field spin glasses
Spin glasses are disordered spin systems invented by theoretical physicists in the early 70's. The aim is to describe the strange magnetic behaviors of certain alloys. Over the past decades, physicists' investigation has generated a series of methodologies and predictions. In the community of mathematics, spin glass models are purely probabilistic objects that present highly complex random structures. The general aim of this research project is to pursue mathematical investigation of physical phenomena including the complexity of the random Hamiltonian, the structure of the Gibbs measure and t