Craig Citro
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350

Currently: Google

Mathematical Interests: Modular forms, number theory, and arithmetic geometry, particularly computational and p-adic aspects.

gmail: craigcitro

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:
  • What's Cython? Northwest Python Day, UW, January 31, 2009. pdf
  • 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, 2009. pdf
  • Sage: Introduction and Status Report, Sage Days 11, UT Austin, November 7, 2008. pdf sws
  • Enumerating mod p Hecke eigenforms.
    • UW Number Theory and Computation Seminar, October 31, 2008. pdf
    • Computations with Modular Forms, Heilbronn Institute, Bristol, UK. August 19, 2008. pdf
  • Sage, Statistics, and (a little) Number Theory, UCLA Statistics Colloquium, June 3, 2008. pdf
  • 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, MA. pdf
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.

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 October 2008).


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, here 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 I'm also an avid Cython user, and I'm planning on contributing some code to Cython as soon as my thesis is turned in.

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:


In Fall 2009, I'm teaching two sections of Math 324, Multivariable Calculus. The webpage for both courses is here.

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 course.

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 HTML.

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 wife Asia. Here's a picture of our adorable daughter, with thanks to Nathan Ryan 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 climbing, and his climbing page is really impressive.

I was featured in the UCLA Graduate Quarterly, which you can find online here. The article got picked up by UCLA Spotlight, so for about two weeks, I was featured on the UCLA homepage (

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 won third place.