My research interests are in the areas of diophantine geometry, arithmetic dynamics, and algebraic number theory.
I work on theoretical as well as computational aspects of these subjects.

Publications

Computing points of bounded height in projective space over a number field.pdf

To appear in Mathematics of Computation.

Preperiodic points for quadratic polynomials over quadratic fields.pdf

With John Doyle and Xander Faber. New York J. Math. 20 (2014) pp. 507-605.

Computing algebraic numbers of bounded height.pdf

With John Doyle. To appear in Mathematics of Computation.
An implementation of the main algorithm is included in Sage.

Preprints

  • “Squarefree parts of polynomial values”. Submitted.view on arXiv

Papers in preparation

  • “Preperiodic points for quadratic polynomials over quadratic fields, III”. With John Doyle and Joseph Wetherell.
  • “A local-global principle in the dynamics of quadratic polynomials”