Gulay holds a PhD from the University of Edinburgh. Her thesis, titled 'governance of disputed maritime areas' focused on the normative and institutional frameworks within which disputed maritime areas exist, arguing that the management of disputed maritime areas and the dispute between states is a process that includes other actors and institutions, which all contribute to the governance of disputed maritime areas. In this context, her thesis explored the role of regional sea bodies and regional fisheries management organisations in relation to environmental protection and fisheries.
Gulay has broad interests in international law and politics and environmental protection.
Her current research interests include interinstitutional cooperation and coordination between the processes of the new treaty regime in areas beyond national jurisdiction (Biodiversity Beyond National Jurisdiction) and existing ocean governance institutions (regional sea bodies and regional fisheries management organisations).
Gulay's research includes international environmental law, marine environmental law and the interplay between international and domestic environmental law. She is also interested in the role of different actors in environmental governance.