### 2-Group Belyi Maps (thesis)

Galois Belyi maps with monodromy group a 2-group. If you don’t know what a Belyi map is (and you are curious) take a look at my poster on dessins d’enfants.

Past talks on this topic:

JMM Special Session on Number Theory, Arithmetic Geometry, and Computation

Maine-Quebec Number Theory Conference

Maine-Quebec Slides

Publication and other resources:

*
2-Group Belyi Maps
*

thesis

thesis defense

github

dessin-explorer.org

jigglegraph

nonheirarchicaljigglegraph

arXiv (in progress)

### Computing Canonical Rings of Hilbert Modular Forms

I worked on a large (10 person) team to implement techniques to compute canonical rings of Hilbert modular forms. I was responsible for the data structure to store and compute with Fourier expansions of Hilbert modular forms necessary to support these computations.

Publication and other resources:

*
Computing Canonical Rings of Hilbert Modular Forms
*
(in progress)

github

arXiv (in progress)

### A Database of Belyi Maps

In this paper, we compute a database of thousands of Belyi
maps up to degree 9.
On top of the group effort to compute an exhaustive list of Belyi
maps, my main responsibility in this project was implementing the database
backend using Magma
(see repository below) to save the results.
I then worked in a team of 4 to migrate the data over to the
*L-functions and Modular Froms Database*
LMFDB

This paper was awarded the Selfridge Prize in Number Theory at ANTS-XIII

Past talk on this topic:

Simons Collaboration Short Talks

(Cambridge, MA, August 2018)

Slides

Publication and other resources:

*
A Database of Belyi Maps
*
(with
Sam Schiavone,
Jeroen Sijsling, and
John Voight)
*
Conference proceedings for ANTS-XIII,
The Open Book Series 2 (2019)
*
Mathematical Sciences Publishers, 2019

Article

arXiv

github

LMFDB

### Understanding the cost of dermatologic care: A survey study of dermatology providers, residents, and patients

Using R, I ran the statistical analysis for survey results in this dermatology study and generated Likert scale visualizations to analyze the data.

Publication and other resources:

*
Understanding the cost of dermatologic care: A survey study of dermatology providers, residents, and patients
*
(with
Aaron Steen,
Julianne Mann,
Valerie Carlberg,
Alexa Kimball,
and Eric Thompson)
*
Journal of the American Academy of Dermatology
*
76.4 (2017) pp. 609-617. Elsevier, 2017

JAAD article

cost.R

providers.R

residents.R

### Numerical calculation of three-point branched covers of the projective line

In this paper, we implement a general numerical method to compute Belyi maps using power series expansions of modular forms. I implemented code to visualize Belyi maps as (equivalent) dessins d’enfants conformally embedded in the hyperbolic unit disk. My code produced figures (such as the one at the top of this page) drawn using PSTricks.

Publication and other resources:

*
Numerical calculation of three-point branched covers of the projective line
*
(with
Michael Klug
Sam Schiavone,
and
John Voight)
*
LMS Journal of Computation and Mathematics
*
17.1 (2014) pp. 379-430.
London Mathematical Society, 2014

arXiv

LMS article