Research

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)

Preprints:

  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: