Lloyd James Peter Kilford

Lloyd in black and white

Academic stuff

BSc & ARCS, Imperial College, University of London, August 1999.
PhD & DIC, Imperial College, University of London, November 2002.
Bateman Research Instructor at the California Institute of Technology, September 2002 -- July 2004.
Visitor at the Max-Planck-Institut fuer Mathematik, August 2004 -- September 2004.
Fellow at Merton College, Oxford (and member of the Mathematical Institute and the Number Theory Group), September 2004 -- September 2007.
Research Fellow at the University of Bristol, September 2007 --.

Research Interests

I am interested in Number Theory; more specifically in such topics as (the arithmetic of) Modular Forms, Elliptic Curves and Arithmetic Algebraic Geometry -- especially the computational aspects of these subjects. I often use computer algebra packages like MAGMA or PARI/GP or SAGE in my work.

I am listed as one of the many contributors to SAGE 4.0.

At the moment I am working on Hecke operators acting on quaternionic modular forms, and considering certain non-Gorenstein Hecke algebras. I am also considering how best one should approximate certain Hecke operators acting on classical modular forms of level p, where X_0(p) has genus 1.

Here are some programs for computing the Hecke operator U_p on quaternionic modular forms.

Here is some code to calculate U_p acting on overconvergent p-adic modular forms, for p such that X_0(p) has genus 1 (in other words, p = 11, 17 or 19).


I taught the course Introduction to Modular Forms in Oxford, as a trial for an undergraduate course to run in 2005--2006, and as a graduate course again in 2006--2007.

I taught the Part C course Introduction to Modular Forms; the lectures were at noon on Tuesdays and Fridays in the Mathematics Institute in Oxford.

In my previous post at Caltech, I taught courses in graduate algebra, Galois theory, elliptic curves for undergraduates and number theory.


I have written a book, Modular Forms: A classical and computational introduction, available on Amazon. It is a graduate-level introduction to the theory of modular forms, starting with the construction of Eisenstein series and working up to the action of Hecke operators. It also covers the computational side of the theory, and shows how SAGE and MAGMA can be used to compute modular forms.

The cover was created using SAGE by Tomas Boothby; I am very grateful to him for his work.

Snazzy book cover
I am maintaining an errata list; please contact me if you find other errors.


Professional information

Mathematical Links

We can only see a short distance ahead, but we can see plenty there that needs to be done. - Alan Turing.

This page last modified by L. J. P. Kilford
Tuesday, 09-June-2009 10:39:00 BST