Department of Mathematics
University of Washington
Seattle, WA 98195-4350
Mathematical Interests: Modular forms, number theory,
and arithmetic geometry, particularly computational
and p-adic aspects.
Teaching, Fall 2009: Math 324
Most of my work is about modular forms, abelian varieties, and their
associated Galois representations
and p-adic L-functions. I'm particularly interested in
explicit computational methods for working with these objects, and in
fact, for all kinds of related (and many not-so-related) computational
questions that come up. As a result, I've become a regular contributor to
Sage, a free and open-source
math software system.
Here's a list of my papers and preprints:
Here are slides from some of the talks I've given over the last few years:
- David S. Wise,
Craig L. Citro,
Joshua J. Hursey,
Fang Liu, and
Michael A. Rainey.
A Paradigm for Parallel Matrix Algorithms: Scalable Cholesky
In J. C. Cuhha and P. D. Medeiros (Eds.),
Lecture Notes in Computer Science 3648,
Berlin: Springer (August 2005), 687--698.
L-invariants of adjoint square Galois representations coming
from modular forms. Int. Math. Res. Notices, Volume 2008,
Art. ID rnn048. Author's version
L-invariants of CM Hecke characters over Q and the
Ferrero-Greenberg Theorem. (Submitted.)
Enumerating Hecke eigensystems of
mod p modular forms. (In preparation.)
Craig Citro. The search for level one companion forms. (In
I've also given a huge number of talks in our student number theory
seminar at UCLA (as well as a few here at UW). Scans of any
interesting notes will appear here as I make it through the massive
stack of my handwritten notes that need to be scanned.
- What's Cython? Northwest Python Day, UW, January 31,
- What does Sage do?, with William Stein. Sage Days 12,
UC San Diego, January 21, 2009. pdf
Sage: Open Source Math Software UW Applied and
Computational Math Sciences Seminar, January 8,
- Sage: Introduction and Status Report, Sage Days 11, UT
Austin, November 7, 2008. pdf
- Enumerating mod p Hecke eigenforms.
- UW Number Theory and Computation Seminar, October 31,
- Computations with Modular Forms, Heilbronn Institute,
Bristol, UK. August 19, 2008.
- Sage, Statistics, and (a little) Number Theory, UCLA
Statistics Colloquium, June 3, 2008.
- Analytic L-invariants coming from modular forms.
UCLA Number Theory Seminar, May 19, 2008.
- Modular Forms in Sage: a Status Report, Sage Days 5, Clay
Math Institute, Cambridge,
In the Spring of 2004, we ran a graduate student seminar where we read
Deligne and Serre's paper on modular forms of weight one. Since the
original was in French, we decided to translate
it. Here is our translation, which was done
by Curtis Paul and myself, with comments from everyone else in the
seminar. Feel free to send me any additional corrections.
When I redesigned the UCLA Number Theory Group webpage, I
wrote this guide to being a grad student
in number theory at UCLA.
Finally, here is a link to my academic CV (from
I work on a lot of problems with a large computational component,
partially because they're the kinds of problems I find interesting,
and partially because I just love computing. In particular, I've
gotten quite involved in working
on Sage. Sage is a free and open
source math software package, whose goal is to be a viable alternative
to the big math software packages (Magma, Mathematica, Maple, Matlab).
I've done lots of work on Sage, much of it to do with modular forms
and number theory. (If you're curious,
is a link to my very first commit, back in 2006.)
I've also worked on other random parts of the
library, because it's just a lot of fun. I can often be found on our
dev channel, #sage-devel on irc.freenode.net. I'm
also an avid Cython user, and I'm
planning on contributing some code to Cython as soon as my thesis is
I've produced some tables of interesting data (especially
related to some of the papers above), as well as a few independent
pieces of software. Links will eventually end up here.
I've organized a bunch of conferences over the last few years, all
related to Sage. Here are some links:
- Sage Days 15,
UW, Seattle, WA. May 16-21, 2009.
- Sage Days 12, UCSD,
San Diego, CA. January 21-24, 2009.
- Sage Days 11, UT
Austin, Austin, TX. November 7-10, 2008.
- Sage Days 7, IPAM,
UCLA, February 5-9, 2008.
- Sage Days 3, IPAM,
UCLA, February 17-21, 2007.
In Fall 2009, I'm teaching two sections of Math 324, Multivariable
Calculus. The webpage for both courses
In Spring of 2008, I was awarded
a CUTF fellowship to design
and teach my own course. I taught a course on elliptic curves,
called Elliptic curves in pure mathematics and the real world.
Here is a link to the webpage for the
In the Fall 2006 and Winter 2007, I was a TAC (TA Consultant) for Math
495, which is the TA training course in the Math
department. Unfortunately, it seems that the course webpage has gone
the way of the PS/2 slot, but this page
has what are probably the world's shortest crash courses on LaTeX and
At UCLA, I've TAed for Number Theory (Math 111), Abstract Algebra (110A, 110B),
Linear Algebra (115A and 115AH), Discrete Math (61), Differential
Equations (33B), Multivariable Calc (32B), and the first-year Calculus
sequence (31A, 31B). When applying for jobs, I calculated that my
overall TA evaluation score for my time at UCLA was 8.2/9.0, which I
was pretty happy with.
Here is a link to the teaching
statement I wrote as part of my UW application.
When I was an undergrad, I was a TA for two semesters of the Intro to
Computer Science for CS majors course, once for the "regular" and once
for the honors version (CSCI C211 and H211, respectively).
I spent the summer of 2000 working
at IMACS, teaching Computer
Science and Computer Enrichment classes to K-12 students. I have an
endless number of good things to say about IMACS, so feel free to ask
me about if you'd like to know more.
About Me / Miscellaneous
I grew up in Plantation, Florida. There were a number of things I
liked about it — especially meeting
Ryan Newton at an
early age. However, the weather is so horrific that I'm unwilling to
visit for very long, to my family's great dismay.
I got married on June 9, 2008 to my lovely
Our daughter, Sophie Grace Citro, was born on July 10, 2009.
Here's a picture, with thanks to
and his wife Rachel for the awesome onesie:
I tend to enjoy lots of outdoorsy things, particularly rock climbing,
hiking, snowshoeing, and biking. My friend Will got me started on
page is really impressive.
I was featured in the UCLA Graduate Quarterly, which you can find
online here. The
article got picked up
Spotlight, so for about two weeks, I was featured on the UCLA
I own a lot of books. In 2007, I entered a book collecting
contest at UCLA, and won with a collection of books related to Emil
Artin's work. This qualified me for an international book collecting
competition run by Fine Books & Collections magazine, in which I