Welcome!

I work as a postdoctoral fellow (Research Scientist) in the Harvard Mathematics Department since September 2021. I am also a member of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. I focus on algorithms for abelian varieties and their moduli spaces, although I am also interested in explicit number theory and algebraic geometry in general. Other Harvard members of the collaboration include Alexander Betts, Alexander Cowan, and Professor Noam D. Elkies.

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 March 8, 2022.

Publications

  • Upper bounds on the heights of polynomials and rational fractions from their values. Acta Arithmetica, to appear. arXiv.
  • Degree and height estimates for modular equations on PEL Shimura varieties. Journal of the London Mathematical Society, to appear. arXiv, Journal link.
  • Sign choices in the AGM for genus two theta constants. Publications Mathématiques de Besançon, to appear. arXiv.
  • 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. arXiv, SpringerLink.

Preprints

  • Counting points on abelian surfaces over finite fields with Elkies's method. arXiv.
  • Certified Newton schemes for the evaluation of low-genus theta constants. arXiv.
  • Evaluating modular equations for abelian surfaces. arXiv.
  • Joint with Aurel Page and Damien Robert: Computing isogenies from modular equations in genus two. arXiv.

Thesis manuscript

Higher-dimensional modular equations, applications to isogeny computations and point counting. Ph.D. thesis, University of Bordeaux, 2021. Official TEL open archive.

Other documents

Internship report on the implementation of the SEA algorithm for crypto-sized elliptic curves (in French): pdf.

Talks (selected)

  • Explicit methods for modularity, Apr. 2022: Asymptotically faster point counting on abelian surfaces. This event replaces the AMS special session that was originally scheduled as part of the JMM in Seattle, Jan. 7-8, 2022. Slides.
  • Bordeaux Math & CS Ph.D. day, Apr. 2022: Isogenies and point counting for curves over finite fields.
  • LFANT seminar, Mar. 2022: Certified Newton schemes for the evaluation of low-genus theta functions. Slides.
  • Simons Collaboration meeting, Mar. 2022: Certified Newton schemes for the evaluation of low-genus theta functions.
  • Simons Collaboration meeting, Oct. 2O21: Software presentation on theta constants and modular equations in genus 2. Slides.
  • Harvard number theory seminar, Oct. 2021: Higher-dimensional modular equations and point counting on abelian surfaces.
  • MIT number theory seminar, Oct. 2021: Higher-dimensional modular equations and point counting on abelian surfaces.
  • Thesis defense, Bordeaux, July 2021: Slides (in French).
  • AGCT, May 2021 (online): On the complexity of modular equations in genus 2. Slides.
  • Geometry seminar, Bordeaux, Nov. 2020 (online): Algorithmic aspects of the moduli space of principally polarized abelian surfaces.
  • C2 days, Nov. 2020 (online): Genus 2 point counting using isogenies. Slides.
  • Computer algebra days (JNCF), Luminy, March 2020: Heights and interpolation of rational fractions. Slides.
  • CARAMBA seminar, Nancy, Feb. 2020: Computing isogenies from modular equations in genus 2.
  • Cryptography seminar, Rennes, Jan. 2020: Computing isogenies from modular equations in genus 2.
  • Lambda PhD seminar, Bordeaux, Oct. 2019: Counting points on elliptic curves over finite fields.
  • AGCT, Luminy, June 2019: Computing isogenies from modular equations in genus 2. Slides.
  • AsiaCrypt, Brisbane, Dec. 2018: Towards practical key exchange from ordinary isogeny graphs. Slides.
  • LFANT seminar, Bordeaux, May 2018: Implementing the SEA algorithm.

Data and software

I have developed a C library called hdme ("Higher-Dimensional Modular Equations") to evaluate Siegel and Hilbert modular equationss for abelian surfaces via analytic methods. The code is available on my GitHub page.

Useful links

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.

I regularly use Flint, Arb, Pari/GP, Magma, and the LMFDB database. You might want to compare performance between Flint and NTL. Here is other software that I find useful:

  • PariTwine (links between Flint, Arb, CMH, Andreas Enge's other libraries and Pari),
  • hcperiods (computation of period matrices of hyperelliptic curves),
  • AVIsogenies (isogeny computations using algebraic theta constants).