Welcome!

PortraitI 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.

Preprints

Publications

  • 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.

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.

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.

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).

Talks

  • Joint Math Meetings (JMM), Boston, Jan. 2023: Certified quasi-linear algorithms for the evaluation of theta functions in low genus.
  • Geometry and Effective algebra seminar, Rennes, Nov. 2022: Computing isogeny classes of principally polarized abelian surfaces over the rationals.
  • Cryptography seminar, Rennes, Nov. 2022: Analytic techniques for isogeny graphs of abelian surfaces.
  • CARAMBA seminar, Nancy, Nov. 2022: Theta functions and isogenies between abelian surfaces.
  • 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.