Steven Sam works at the interface of combinatorics, representation theory and algebraic geometry.

An underlying theme of his work involves commutative algebra with a focus on the theory of representations, in particular the emerging area of representation stability.  Representation theory is the study of symmetries, and concerns all possible ways that the same symmetries can act on different objects.

A major study within representation theory concerns invariants that are fixed by all of the symmetries. Sam with Snowden introduced an invariant theory for twisted commutative algebras which is of widespread interest. Sam has made substantial contributions to understanding finiteness properties of sequences of representations.  In the course of his work Sam solved the Lannes-Schwartz artinian conjecture.