Research

I am currently an Assistant Professor of mathematics at High Point University. I was a math Ph.D. student at the University of North Carolina at Chapel Hill working with Professor Dima Arinkin. For a broad summary of my current theoretical mathematics research and research interests, take a look at my Research Statement. My Master's work focused on the formal reduction of differential operators to a canonical form. The paper is based on the classical papers by Turritin and Levelt, put into more modern language as given in books by Malgrange (as well as van der Put/Singer). A copy of the paper can be found here. My current research deals with local integral transforms and how they act on vector spaces with either differential or difference operators, specifically focusing on calculating the local Fourier and Mellin transforms. My doctoral work was completed in May 2011, and my paper "Explicit calculations of local formal Fourier transforms" was accepted for publication in the journal Arkiv for Matematik, and can be found online here. The paper corroborates previous independent results by Sabbah and Fang, but proves them in a different way. The second half of my dissertation, "Explicit calculations of the local formal Mellin transform", has been submitted for publication. A pre-print can be found here.

I have also recently been dabbling in research related to voting theory and recreational mathematics. Some work I did with a couple undergraduates (Nick Zayatz and David Naylor) on the prevalence of monotonicity anomalies in real-world data is currently in preparation. I have also begun preliminary research on the structure of the different end-behaviors found in the game Enemy Protector.

I have also been involved in numerous aspects of the scholarship of teaching and learning, including writing projects and flipping the classroom. A paper I co-wrote with Elin Farnell and Julianna Connelly Stockton, "Mat-Rix-Toe: Improving writing through a game-based project in linear algebra" has been published in the journal PRIMUS. Another paper (with Laurie Zack, Jenny Fuselier, Ron Lamb, and Karen O'Hara) titled "Flipping Freshman Mathematics" has also been accepted for publication.

Publications

  • (with N. Zayatz and D. Naylor) Lack of monotonicity anomalies in real-world data, in preparation.
  • Explicit calculation of local formal Mellin transforms, submitted for publication.
  • (with L. Zack, J. Fuselier, R. Lamb, and K. O'Hara) Flipping Freshman Mathematics, accepted for publication in PRIMUS.
  • (with E. Farnell and J. Stockton) Mat-Rix-Toe: Improving writing through a game-based linear algebra project, PRIMUS, 24(6) (2014), 491-512. DOI: 10.1080/10511970.2013.876476
  • Calculation of local formal Fourier transforms, Arkiv for Matematik, 51 (2013), 71-84 DOI: 10.1007/s11512-011-0156-2