Samantha Kirk’s research focuses on the representation theory of infinite-dimensional Lie algebras. These algebras play an important role in many areas of mathematics and physics including combinatorics, number theory, differential equations, and quantum mechanics. Kirk’s work involves taking Lie algebras (which can have complicated structures) and reinterpreting their elements as matrices that satisfy certain properties. By working with matrices instead of abstract structures, Kirk uses tools from linear algebra to unlock the secrets hidden behind Lie algebras. Kirk’s current projects aim to provide more insight into the structure of infinite-dimensional Lie algebras and their applications.