I am a postdoctoral fellow (Research Scientist) in the Department of Mathematics at Harvard. I am also a member of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. The other Harvard members of the collaboration are Alexander Betts, Alex Cowan, and Prof. Noam D. Elkies.
My research is about algorithms for abelian varieties and their moduli spaces, although I am also interested in explicit number theory and algebraic geometry in general. I obtained my Ph.D. in 2021 in Bordeaux under the supervision of Damien Robert and Aurel Page, in the home of the extraordinary Pari/GP software. Before that, I was a student at École normale supérieure (ENS) in Paris. Here is a more complete curriculum vitae.
This webpage was last updated on January 30, 2023.
- Joint with Raymond van Bommel, Shiva Chidambaram and Edgar Costa: Computing isogeny classes of typical principally polarized abelian surfaces over the rationals. arXiv.
- Joint with Eran Assaf, Angelica Babei, Ben Breen, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight: A database of basic numerical invariants of Hilbert modular surfaces. arXiv.
- Counting points on abelian surfaces over finite fields with Elkies's method. arXiv.
- Evaluating modular equations for abelian surfaces. arXiv.
- Joint with Aurel Page and Damien Robert: Computing isogenies from modular equations in genus two. arXiv.
- Certified Newton schemes for the evaluation of low-genus theta functions. Numerical algorithms (2022). arXiv, journal.
- Degree and height estimates for modular equations on PEL Shimura varieties. Journal of the LMS 105 (2022), 1314--1361. arXiv, journal.
- Upper bounds on the heights of polynomials and rational fractions from their values. Acta Arith. 203 (2022), 49--68. arXiv, journal.
- Sign choices in the AGM for genus two theta constants. Pub. Math. Besançon, Algèbre & Th. des nombres (2022), 37--58. arXiv, journal.
- Joint with Luca De Feo and Benjamin Smith: Towards practical key exchange from ordinary isogeny graphs. In T. Peyrin and S. Galbraith (editors), Advances in Cryptology - AsiaCrypt 2018, IACR, 365-394. arXiv, journal.
Higher-dimensional modular equations, applications to isogeny computations and point counting. Ph.D. thesis, University of Bordeaux, 2021. Official TEL open archive.
Internship report on the implementation of the SEA algorithm for crypto-sized elliptic curves (in French): pdf.
Data and software
- hdme: a C library for the evaluation of modular equations of Siegel and Hilbert type for abelian surfaces. GitHub.
- acb_theta: a module for the Arb library featuring a certified implementation of quasi-linear algorithms for theta functions in any dimension. GitHub. This is work in progress, which should soon be merged into the Arb master branch.
Enea Milio's webpage contains examples of modular equations of Siegel and Hilbert type (discriminants 5, 8 and 12) in different coordinates. Compared to these, the elliptic modular polynomials from Andrew Sutherland's database do look tiny.