I am interested in the intersection of Ring Theory and Linear Algebra. More specifically, I study algebras which are linearly spanned by elements of various types and their embeddings as infinite matrix algebras. Furthermore, I am interested in in exploring these topics in combinatorially defined algebras such as Leavitt path algebras .

I am also interested in Algebraic Coding Theory, specifically generalizations of Reed-Solomon codes and their applications to problems of communication and distributed storage.

I keep a semi-updated blog of my research activities and other odds and ends here: InOverMyHead Math Blog

Research Statement

Peer-Reviewed Publications:

  1. (With S. R. Lopez-Permouth) On the Associativity of Infinite Matrix Multiplication. American Mathematical Monthly. (arXiv link).

  2. (With S. R. Lopez-Permouth) Algebras Having Bases Consisting Solely of Strongly Regular Elements. Journal of Pure and Applied Algebra.(preprint)

  3. (With S. R. Lopez-Permouth) Bases of Leavitt Path Algebras with only Strongly Regular Elements. Communications in Algebra. (preprint)

  4. Ideal Extensions and Directly Infinite Algebras. Pure and Applied Algebra. (link)


  1. (With D. Herden and A. Pasi) Forcing a Basis into Aleph1 Free Groups.

  2. Ideal Extensions and Directly Infinite Matrix Algebras. (arXiv link)

  3. A Family of Almost Invertible Infinite Matrices. (arXiv link)

Thesis and Dissertations: