Wyart's research encompassed field such as the architecture of allosteric materials, the theory of
deep learning, the elasticity and mechanical stability in disordered solids, the granular and suspension flows, the marginal stability at random close packing and other glasses, and the yielding transition and elasto-plasticity. In particular, some of his recent research is focused on the classification of the elementary excitations controlling the linear and the plastic response in
amorphous materials. He has discovered that some of these excitations are marginally stable in the solid phase. This marginality fixes key aspects of structures, and suggest that the density of excitations presents a pseudo-gap. These concepts are important to understand low-temperature properties of glasses, the
rheology of dense granular and suspension flows, the elasticity close to the jamming transition, the production transition in foams or metallic glass, == Distinctions ==