He has been interested, in particular, in the interplay between fluctuations, geometry and statistical dynamics in condensed matter systems such as magnets, superfluids, liquid crystals, superconductors, polymers, turbulent fluids and metallic glasses.

A variety of predictions associated with this two-state freezing process have now been confirmed in experiments on two-dimensional colloidal assemblies, thin films and bulk smectic liquid crystals.

Nelson's research also includes a theory of the structure and statistical mechanics of metallic glasses and investigations of "tethered surfaces,” which are two-dimensional generalizations of linear polymer chains.

Flexural phonons lead a remarkable low temperature flat phase in these fishnet-like structures, with predictions of strongly scale-dependent elastic constants such as the two-dimensional Young's modulus and the bending rigidity of atomically or molecularly thin materials such as a free-standing sheets of graphene and MoS2.

David Nelson's recent investigations have focused on problems that bridge the gap between the physical and biological sciences, including dislocation dynamics in bacterial cell walls, range expansions and genetic demixing in microorganisms and localization in asymmetric sparse neural networks.