Greg Stevenson works in algebraic geometry, homological algebra, and the representation theory of algebras. He has made significant contributions to all three branches of mathematics. One aspect of his work in geometry concerns the theory of tensor triangulated categories. This is a modern abstraction of classic algebraic geometry, which has attracted the attention of many leading geometers. Greg Stevenson has used advanced homological methods to establish several fundamental properties of such categories.

In representation theory, Greg Stevenson's work on singularity categories has widened the scope for constructing such categories and deepened our understanding of their invariants. He has also constructed new combinatorial models of representation theoretical categories. In 2016, he won the prestigious International Conference on Representations of Algebras Award for "[introducing] fundamental new ideas in the representation theory of algebras, based on geometric ideas and successfully using the framework of triangulated categories."

Greg Stevenson obtained his PhD degree from the Australian National University in 2011 under the supervision of Amnon Neeman. He held Humboldt Postdoctoral Fellowships at Bielefeld, was a postdoctoral research fellow at the MSRI Berkeley, and was appointed to a lectureship at the University of Glasgow in 2017.