Wolfram is an algebraist who attained his PhD at the University of Waterloo under the supervision of Ross Willard. After initially working in Canada, he received a prestigious Marie Curie Fellowship and moved to the Center of Algebra, University of Lisbon, where he was the principal investigator for the research project “Dualizability of Algebras from Congruence-Permutable Varieties”, funded by the European Union's Research Executive Agency and the Foundation for Science and Technology of Portugal. He stayed at the Center of Algebra under a Visiting Science Fellowship before joining the University of Hull in 2015.
Wolfram's research examines connections between algebras (groups, semigroups, independence algebras, and more general, algebras in the meaning of Universal Algebra) and other mathematical objects that have a natural connection to the algebras. These objects are combinatorial structures, such as graphs or automata, topological spaces, and more complicated objects such as relational topological structures. Wolfram's work establishes properties of algebras using the associated objects, and vice versa.