PIMS-CNRS Post-doc at UCalgary, under Renate Scheidler.
Mathematics, computer science, cryptography.
Algorithmic number theory, Drinfeld modules, computer algebra.

Orcid 0000-0003-3858-071X Github kryzar first dot last at ucalgary dot ca Office MS 462

Antoine Leudière

Research Software Service Students Teaching Talks Education

Research

Published

PhD Thesis

Morphisms of Drinfeld Modules and their Algorithms. (link)

Under Pierre-Jean Spaenlehauer and Emmanuel Thomé. At INRIA team Caramba, Loria, Université de Lorraine, Nancy, France. Thesis defended on September 16th, 2024. Jury consisting of Xavier Goaoc (president), Alain Couvreur (examiner), Éric Schost (examiner), Cécile Armana, Elena Berardini, as well as Pierre-Jean Spaenlehauer and Emmanuel Thomé.

Software

SageMath

SageMath developer. Started the official SageMath implementation of Drinfeld modules (first issue). First version merged with version 10.0, with the help of David Ayotte, Xavier Caruso and Joseph Musleh (account 1, account 2)—see the ISSAC Software presentation of the first version. The project is very active.

Pull requests

  1. Fix Drinfeld module frobenius_endomorphism doc

    PR 40575. Opened by kryzar on 2025, August 11. Merged 2025, August 16. +5-5 lines.
  2. Fix DrinfeldModule is_isomorphic method absolutely' flag

    PR 38303. Opened by kryzar on 2024, June 28. Merged 2024, July 24. +14-2 lines.
  3. Delete _check_rank_two method for Drinfeld modules

    PR 38199. Opened by kryzar on 2024, June 11. Merged 2024, July 24. +0-21 lines.
  4. New algorithms to compute the characteristic polynomial of the Frobenius endomorphism of a Drinfeld module

    PR 38174. Opened by kryzar on 2024, June 8. Merged 2024, September 22. +415-68 lines.
  5. Enhance documentation of Drinfeld module Potemine j-invariants

    PR 37630. Opened by kryzar on 2024, March 19. Merged 2024, March 31. +25-6 lines.
  6. Make rank return an Integer object

    PR 35519. Opened by kryzar on 2023, April 15. Merged 2023, May 22. +34-4 lines.
  7. Drinfeld modules

    PR 35026. Opened by kryzar on 2023, February 8. Merged 2023, March 13. +3538-0 lines.

Code reviews

  1. Add a method for changing field of definition of Drinfeld modules

    PR 40706. Opened by xcaruso on 2025, August 27. Merged 2025, October 6. +63-37 lines.
  2. Fix bug in SkewPolynomialRing when twisting morphism is trivial

    PR 40697. Opened by xcaruso on 2025, August 26. Merged 2025, September 21. +114-44 lines.
  3. Ore modules with poles

    PR 40674. Opened by xcaruso on 2025, August 24. Merged 2025, October 6. +393-32 lines.
  4. Fix documentation for Drinfeld modules

    PR 40599. Opened by xcaruso on 2025, August 16. Merged 2025, August 27. +293-294 lines.
  5. Hom spaces between Drinfeld modules

    PR 40440. Opened by xcaruso on 2025, July 18. Merged 2025, August 27. +853-221 lines.
  6. Remove useless limitations in Drinfeld modules

    PR 40436. Opened by xcaruso on 2025, July 17. Merged 2025, August 27. +220-221 lines.
  7. gcd and lcm of isogenies of Drinfeld modules

    PR 40434. Opened by xcaruso on 2025, July 17. Merged 2025, August 27. +313-221 lines.
  8. Constructor for the Carlitz module

    PR 40433. Opened by xcaruso on 2025, July 17. Merged 2025, August 27. +423-223 lines.
  9. Implement relative Frobenius for Drinfeld modules

    PR 40432. Opened by xcaruso on 2025, July 17. Merged 2025, August 27. +284-221 lines.
  10. Use the variable name τ instead of t for Drinfeld modules

    PR 40430. Opened by xcaruso on 2025, July 17. Merged 2025, August 27. +220-221 lines.
  11. Limit the use of RingExtensions in Drinfeld modules

    PR 40421. Opened by xcaruso on 2025, July 16. Merged 2025, July 25. +45-63 lines.
  12. Method A-field for Drinfeld modules

    PR 40420. Opened by xcaruso on 2025, July 16. Merged 2025, July 25. +53-2 lines.
  13. Class polynomial for Drinfeld modules

    PR 39215. Opened by xcaruso on 2024, December 28. Merged 2025, February 21. +283-4 lines.
  14. Add keyword prec for exponential and logarithm of Drinfeld modules

    PR 39214. Opened by xcaruso on 2024, December 28. Merged 2025, February 21. +47-18 lines.
  15. Add support for pseudomorphisms

    PR 38650. Opened by xcaruso on 2024, September 12. Merged 2025, February 21. +1027-10 lines.
  16. Extend Drinfeld modules to support fields constructed as univariate quotients

    PR 37923. Opened by ymusleh on 2024, May 2. Not merged yet. +96-13 lines.
  17. Implement Drinfeld modular forms

    PR 36538. Opened by DavidAyotte on 2023, October 25. Merged 2024, June 1. +1481-2 lines.
  18. Implement Goss polynomials of Drinfeld modules

    PR 35991. Opened by DavidAyotte on 2023, July 26. Merged 2023, August 27. +99-0 lines.
  19. Improve morphisms between Drinfeld modules

    PR 35527. Opened by xcaruso on 2023, April 16. Merged 2023, July 20. +1059-108 lines.
  20. Add method for computing isogenies between Drinfeld modules

    PR 35386. Opened by ymusleh on 2023, March 30. Merged 2025, August 27. +369-0 lines.
  21. add missing colon in `finite_drinfeld_module.py`

    PR 35287. Opened by DavidAyotte on 2023, March 14. Merged 2023, April 1. +1-1 lines.
  22. Implement characteristic polynomial computation for Drinfeld modules of any Rank

    PR 35269. Opened by ymusleh on 2023, March 13. Merged 2023, November 5. +349-90 lines.
  23. Implement the logarithm and the exponential of a Drinfeld module

    PR 35260. Opened by DavidAyotte on 2023, March 10. Merged 2023, May 22. +247-0 lines.
  24. Implement basic j-invariants of Drinfeld modules

    PR 35057. Opened by DavidAyotte on 2023, February 10. Merged 2023, July 30. +513-25 lines.

dEAduction

Worked on the first version and designed & developed the graphical interface of dEAduction, a Free and Open Source Software for mathematics undergrad students. We augmented the LEAN proof assistant with a dynamical and graphical interface to help students writing basic proofs. The software is now used in various French universities. It was created by Frédéric Le Roux.

Service

Ktorphée

Created and co-run Ktorphée, a mathematics seminar which takes place at night in the catacombs of Paris. Presentations are purely oral, and sessions include exploration of the catacombs. This setting favours transmitting core ideas in a context (without neglecting formal technique) of direct and respectful discussion. List of speakers on the website.

Knowledge should be free

Created knowledgeshouldbefree.org, a website hosting high quality lecture notes. It was motivated as a tribute to my former teacher Alain Kraus, who gracefully accepted to open his archives for this project. The project is faithful to University spirit: free, open and rigorous.

Organization

Students

Supervision (unofficial) of UCalgary PhD student Andrew Cha, on algorithmics of Drinfeld modules. With Renate Scheidler.

Teaching

Mines de Nancy

The Mines de Nancy (National Higher School of Mines of Nancy) is an engineering school. Taught in their computer science department during the three years of my PhD thesis.

  • Algorithmes et complexité

    Coordinated by Xavier Goaoc. Taught in 2022. Level: L3 (third year).
    Introduction to algorithms and complexity, from a formal point of view.
  • Database essentials

    Coordinated by Yannick Toussaint. Taught in 2022. Level: M1 (fourth year).
    Introduction to databases.
  • Operations Research

    Coordinated by Pierre-Étienne Moreau. Taught in 2021, 2022, 2023. Level: L3 (third year).
    Python course, emphasis on efficient manipulation of data structures.
  • Programmation et structure de données

    Coordinated by Bernardetta Addis. Taught in 2022, 2023. Level: L3 (third year).
    Various topics on linear programming and graph optimization.

UCalgary

Teaching in the UCalgary mathematics department as part of my post-doctoral fellowship.

  • Linear Methods I (math 211)

    Coordinated by Carlo Maria Scandolo. Taught in 2025. Level: 1st year.
    Introduction to linear algebra.

Talks

  • Point counting without points

    René 25, Celebrating the research interests of René Schoof. GAATI, Punaauia, French Polynesia. August 21, 2025.
  • Point counting on Drinfeld modules

    Ouragan seminar. IMJ-PRG, Paris, France. July 8, 2025.
  • A computation on Drinfeld modules

    Number Theory and Algebraic Geometry Seminar. Simon Fraser University, Vancouver, Canada. May 29, 2025.
  • Computations in positive and zero characteristic

    Alberta Number Theory Days XVI. BIRS, Banff, Canada. May 3, 2025.
  • Abstract nonsense in number theory: replacing integers by polynomials

    PIMS post-doctoral fellows summit. UCalgary, Calgary, Canada. April 28, 2025.
  • Elliptic curves, Drinfeld modules, and computations

    Algebra and Number Theory Seminar. UCalgary, Calgary, Canada. March 13, 2025.
  • Contributing to SageMath: a guide for mathematicians

    Number Theory Group seminar. UCalgary, Calgary, Canada. January 29, 2025.
  • Algorithms for Drinfeld modules and their isogenies

    Mathematics for post-quantum cryptanalysis. Eötvös Loránd University, Budapest, Hungary. August 28, 2024.
  • Drinfeld modules for cryptography

    CAIPI Symposium. FRUMAM, Marseille, France. February 23, 2024.
    url
  • Drinfeld modules in SageMath

    ISSAC'23. Tromsø, Norway. July 26, 2023.
  • Drinfeld modules in SageMath

    Journée du D1. Loria, Nancy, France. April 7, 2023.
  • Modules de Drinfeld: action de groupe de classe explicite et implémentation

    Géométrie et algèbre effectives seminar. IRMAR, Rennes, France. September 23, 2022.
  • An explicit CRS-like action with Drinfeld modules

    INRIA LFANT seminar. IMB, Talence, France. June 14, 2022.
  • An explicit CRS-like action with Drinfeld modules

    INRIA GRACE seminar. LIX, Saclay, France. May 30, 2022.
  • Function field analogue of the CRS key exchange

    Journées C2. Hendaye, France. April 19, 2022.
  • Hard Homogeneous Spaces from the Class Field Theory of Imaginary Hyperelliptic Function Fields

    JNCF. CIRM, Luminy, France. February 28, 2022.

Education

Cursus

  • BsC (licence), Mechanics

    Sorbonne Université, 2015-2018.
  • BsC (licence), Musicology

    Sorbonne Université, 2015-2018.
  • BsC 3rd year (L3), Mathematics

    Sorbonne Université, 2018-2019.
  • MsC 1st year (M1), Mathematics

    Sorbonne Université, 2019-2020.
  • MsC 2nd year (M2), Mathematics (applied algebra)

    Université Paris Saclay, 2020-2021.
  • PhD, Computer science

    Université de Lorraine, 2021-2024.

Grants

  • DrEAM (Université de Lorraine)

    Worth 4500 €. Funding for a three months visit to Renate Scheidler at the University of Calgary during my PhD. In 2022. link
  • Mitacs Globalink Research Award

    Worth 6000 CAD. Funding for a three months visit to Renate Scheidler at the University of Calgary during my PhD. In 2022. link
  • PIMS-CNRS Post-doctoral fellowship

    Worth 30000 CAD per year, for two years. Partial funding for my post-doctoral fellowship at the University of Calgary. In 2024. link