Greig's research is associated with the 'Open Marxism' and 'science as practical criticism' approaches to political economy. His critical engagement with these approaches has been in two areas. First, he has extended its empirical focus into the politics of global competitiveness in the developing world and at the urban scale, and into the European South in the context of the Eurozone crisis and the ensuing decade or more of austerity. Second, he has engaged the approach with theories of the 'production of space', pushing it into new and interdisciplinary areas of theoretical and empirical research in the process.
Greig is currently working on a new book project: 'The Urbanization of Digital Capitalism', focusing on two decades of industrial and urban transformation in Barcelona.
In the recent past, Greig has been involved in three further research projects:
1. Re-thinking the New International Division of Labour
This was a collaborative project, drawing upon the value-theoretical research produced under the auspices of the Centre for Science as Practical Criticism (Buenos Aires). It resulted in an article and a book, co-edited with Guido Starosta, that advances a critical re-examination of the New International Division of Labour thesis, incorporating theoretical and case study chapters by a range of international scholars (published by Palgrave Macmillan).
2. The Limits to Capital in Spain
This was a collaborative project, with Ramon Ribera-Fumaz and Thomas Purcell. The aim of the project was to theorise the development of Spanish capitalism from the 1940s to the present day. This project culminated in the research monograph The Limits to Capital in Spain (Palgrave, 2014).
3. Henri Lefebvre's Marxism
This final project looked at Lefebvre's contemporary relevance for urban research.
Greig's doctoral and immediate post-doctoral research examined the role of international organisations in the process of national state restructuring, with a focus on the Latin American region.