Research

user-297566__180 user-297566__180

Research Interests

I am interested in algebraic geometry and number theory. My advisor is John Voight. Most of my research has centered on computation of explicit equations for Belyi maps. I am also currently working on the following projects.

  • Computing equations for Hilbert modular varieties. (See here for our work so far.)
  • Classifying algebras of low rank and degree over a commutative ring.
  • Gluing curves along their torsion subgroups.

Two other frequent collaborators are Mike Musty and Jeroen Sijsling.

Publications

2. [PDF] [1805.07751]
A Database of Belyi Maps
(with Michael Musty, Jeroen Sijsling, and John Voight),
To appear in the proceedings of ANTS XIII.
1. [PDF] [1311.2081]
[Errata] [Link]
Numerical calculation of three-point branched covers of the projective line
(with Michael Klug, Michael Musty, and John Voight),
LMS J. Comput. Math. 17 (2014), no. 1, 379-430.