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