I’m interested in the application of algebraic techniques to number theoretic questions
My research focuses on using the techniques of $p$adic Hodge theory and $(\phi, \Gamma)$modules to study a number of arithmetic principles. In particular, there is a wonderful conjecture of Bloch and Kato which generalizes both the analytic Class Number Formula and the Birch and SwinnertonDyer conjecture. My work with Matthias Flach has strengthened the evidence for this conjecture in the case of Tate motives over number fields.
I am currently most interested in the properties of supercharacters and their applications to number theory. This is a new area with connections to representation theory and number theory, and presents a number of interesting problems which are accessible to undergraduate researchers and produce interesting graphical representations. I also hope to some day return to the study of nonunique factorization problems in numerical monoids.
Papers:

On the local Tamagawa number conjecture for Tate motives over tamely ramified fields, to appear in Algebra & Number Theory (with Matthias Flach)
 Delta sets of numerical monoids using nonminimal sets of generators Comm. Algebra 38 (2010), no. 7, 2622–2634. (with Scott Chapman, Rolf Hoyer, and Nathan Kaplan).
 Sampling Lissajous and Fourier knots Experiment. Math. 18 (2009), no. 4, 481–497 (with Adam Boocher, Jim Hoste, and Wenjing Zheng).
Doctoral Thesis:
 “On the local Tamagawa number conjecture for Tate motives“, advised by Matthias Flach (2014).
Undergraduate Thesis:
 Determining unitary equivalence to a $3 \times 3$ complex symmetric matrix from the upper triangular form (pdf), advised by Stephan Garcia (2008).