My research is in universal algebra. I am currently studying clonoids. A clonoid from an algebra A to an algebra B is a set of functions from finite powers of A into B that is closed first with respect to composition with term functions of A on the domain side and next with respect to composition with term functions on B on the codomain side. Clonoids have been used in studying equational theories of finite algebras, classifying expansions of algebras, and investigating the computational complexity of Promise Constraint Satisfaction Problems. In the article, Clonoids between modules, Peter Mayr and I investigate clonoids whose source and target are abelian Mal'cev algebras (algebras that are polynomially equivalent to modules). The preprint Structure and Complexity in 2-Nilpotent Mal'cev Algebras connects clonoids to central extensions. In particular, we can understand the structure of a 2-nilpotent Mal'cev algebra by understanding two abelian algebras and a clonoid from one to the other. In the same preprint I also investigate the Subpower Membership Problem, which asks for a fixed algebra, given elements in some power of the algebra, determine if another given element is in the subalgebra generated by these elements. I show that 2-nilpotent Mal'cev algebras of squarefree order have Subpower Membership Problem solvable in polynomial time. Current research aims to extend this result to all 2-nilpotent Mal'cev algebras.

Publications and Preprints