I am a CNRS researcher (chargé de recherche) in mathematics and computer science at LORIA (Université de Lorraine), 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. I am also in charge of organizing the team seminar.
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 under the supervision of Damien Robert and Aurel Page. Before that, I was a student at École normale supérieure (ENS) in Paris. Here is a more complete CV.
This webpage was last updated on Oct. 11, 2024. If you notice any link that doesn’t work, please let me know.
Upcoming events
- On November 14-15 and 28-29, I will be teaching a graduate course on isogeny graphs of elliptic curves and abelian varieties at the University of Luxemburg. More information will be available at https://math.uni.lu/nt/
- Aterlier Pari/GP, Palaiseau, Jan. 6-10, 2025
- FLINT workshop, Palaiseau, Jan. 27-31, 2025
- The CAIPI Symposium will likely be held in Nancy sometime around April or May.
Preprints
Search for all my publications and preprints on arXiv.
- Spanning isogeny classes of principally polarized abelian surfaces with RM. arXiv.
- Joint with Noam D. Elkies: A uniform quasi-linear algorithm for evaluating theta functions in any dimension, in preparation (see the software section below).
- 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.
Publications
- Joint with Raymond van Bommel, Shiva Chidambaram and Edgar Costa: Computing isogeny classes of typical principally polarized abelian surfaces over the rationals. Proceedings of the conference “LMFDB, Computation and Number Theory” (LuCaNT), Contemporary Mathematics, 2023. 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. Proceedings of the LuCaNT conference, Contemporary Mathematics, 2023. 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.
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.
Thesis manuscript
Higher-dimensional modular equations, applications to isogeny computations and point counting. Ph.D. thesis, University of Bordeaux, 2021. Official TEL open archive.
Talks
- 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
- Siegel modular forms in LMFDB workshop at ICERM, Providence, Nov. 16-19, 2023
Other
Internship report on the implementation of the SEA algorithm for crypto-sized elliptic curves (in French): pdf.
