Gay's research interests are anchored in public law and legal philosophy. She is particular interested in constitutionalism, looking at what it is that differentiates 'functioning' constitutional systems from 'failed' systems, with the aim of both strengthening the stability and fairness of functioning systems and the contextual factors that lead to system failure. This ties into her interests in legal history and comparative law, particularly comparative constitutionalism. Her background in criminal appellate work feeds a parallel research interest in issue of justice, in the content and administration of both civil and criminal law (and the grey area inbetween).
She also researches and teaches in the area of Animal Law and is interested in the moral considerateness of all 'sentient' beings, who those might be, and how the legal system ought to properly organise their interactions and on what basis. This extends to environmental and conservation issues, where she has published on the precautionary principle governing human environmental management and on the gnarly moral interface between the moral interests of members of 'pest' sprecies versus those of species at risk. She has lately been researching on the possible grounds for the moral considerateness of AI and what that might mean for public law.