Welcome !

I am a CNRS researcher (chargé de recherche) in mathematics and computer science at LORIA (Nancy, France), in the CARAMBA team led by Emmanuel Thomé. My research centers on algorithms for abelian varieties and their moduli spaces and their applications in public-key cryptography.

From 2021 to 2023, I was a postdoctoral fellow in mathematics at Harvard with Prof. Noam D. Elkies, and a member of the Simons Collaboration on Arithmetic Geometry, Number Theory and Computation. I defended my PhD in 2021 at the University of Bordeaux in the LFANT team under the supervision of Damien Robert and Aurel Page. Before that, I was a student at École normale supérieure (ENS) in Paris.

This webpage was last updated on March 24, 2026. If you notice any link that doesn’t work, please let me know.

Internships

I welcome spontaneous internship or PhD applications in computational number theory/algebraic geometry and isogeny-based cryptography. Prior to contacting me, please note the following:

  • Please follow the guidelines given on the CARAMBA webpage.
  • I am usually away during the summer. Internships starting early in the spring are preferable.
  • Internships are in-person at LORIA. There is a mandatory 3-month delay between the moment we send your file to the administrative staff and the start date of the internship. Corollary: contact me early.
  • Internships are funded.
  • In the case of a PhD, it will be necessary to jointly apply for funding. The application deadline is around April to start the PhD in October (usually). The PhD will be cosupervised with someone more senior.

Upcoming events

Preprints

Search for all my publications and preprints or arXiv. Most of them can also be found on the HAL open archive. See also OrcID for information on published articles.

  • Joint with Noam D. Elkies: Fast evaluation of Riemann theta functions in any dimension. arXiv.
  • Spanning isogeny classes of principally polarized abelian surfaces with RM. arXiv.
  • Counting points on abelian surfaces over finite fields with Elkies’s method. arXiv.
  • Evaluating modular equations for abelian surfaces. arXiv.

Publications

Software

My GitHub account.

  • acb_theta: a module for the FLINT library featuring certified, quasi-linear time algorithms to evaluate Riemann theta functions in any dimension.
  • hdme: a C library for the evaluation of modular equations of Siegel and Hilbert type for abelian surfaces. GitHub.

Students

  • Hugo Nartz (PhD student, from Nov. 2025, cosupervised with Emmanuel Thomé)
  • Alexandre Benoist (M2 internship, March-July 2024, and pre-PhD internship, Sept.-Nov. 2024)
  • Ilan Ehrlich (M2 internship, Nov. 2025 – March 2026)

Teaching

  • Algorithms & Complexity TA, Mines Nancy, Fall 2025.
  • Isogeny graphs of abelian varieties over finite fields. 16-hour graduate mini-course, University of Luxembourg, November 2024. Course notes.
  • Python programming TA, Mines Nancy, Spring 2024.

Manuscripts

  • 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.

Talks

  • CANARI seminar (ex LFANT), Bordeaux, March 2025: Fast evaluation of Riemann theta function in any dimension.
  • FLINT workshop, Inria Saclay, January 2025: Theta functions in FLINT. Slides.
  • MATHEXP seminar, Inria Saclay, November 2024: Fast evaluation of Riemann theta function in any dimension.
  • Leuven Isogeny Days 5, KU Leuven, September 2024: Fast evaluation of genus 2 modular polynomials via theta functions. Slides.
  • NuSCAP meeting, Paris, May 2024: Evaluating theta functions in uniform quasi-linear time in any dimension. Slides.
  • KULB mathematical cryptography seminar, Leuven, May 2024: Modular polynomials for abelian surfaces and related algorithms. Slides.
  • CARAMBA seminar, Nancy, Jan. 2024: Evaluating theta functions in uniform quasi-linear time in any dimension.
  • Journées Arithmétiques, Nancy, July 2023: Isogeny classes of abelian surfaces over the rationals.
  • Arithmetic statistics, Luminy, May 2023: Isogeny classes of abelian surfaces over the rationals.
  • COUNT (Computations and their uses in number theory), Luminy, Feb. 2023: Isogeny classes of abelian surfaces over the rationals (in replacement of Edgar Costa). Slides.
  • Clermont, Caen and Besançon number theory seminars, Feb/Feb/June 2023: Isogeny classes of abelian surfaces over the rationals.
  • 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: Isogeny classes of 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.

Events I participated in organizing