About
I am an Associate Professor at the University of Limoges. My work focuses on algebraic geometry (in particular the arc scheme), differential algebra, and (differential) tropical geometry, and more recently on computer algebra, with applications of Gröbner bases to cryptography.
- 2021–…: Associate Professor (Computer Algebra group), University of Limoges (XLIM).
- 2018–2021: PhD, University of Rennes 1 — advisors: David Bourqui & Julien Sebag (defended on Dec 7, 2020) PhD.
- 2017: Agrégation in Mathematics (rank 17).
- 2014–2018: Department of Mathematics, ENS Rennes.
- 2011–2014: MPSI–MP, Lycée Henri-IV, Paris.
Research (publication)
- A digital signature scheme based on the vector space factorization problem and the MPC-in-the-Head paradigm , P. Gaborit, M. Haiech and R.Neveu, Advances in Mathematics of Communications, Tome 19, no 5 (2025), p. 1433-1459. AMC
- Deformations of solutions of algebraic differential equations, M. Haiech, Annales de l'Institut Fourier, Vol. 74, no 5 (2024), pp. 2187–2229. Journal page
- On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry, S. Falkensteiner, C. Garay-López, M. Haiech, M-P. Noordman, Z. Toghani, F. Boulier — Journal of Symbolic Computation 115 (Mar–Apr 2023), 53–73. ScienceDirect
- The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry, S. Falkensteiner, C. Garay-López, M. Haiech, M-P. Noordman, F. Boulier, Z. Toghani — ISSAC 2020 (Distinguished Paper). arXiv
- On the nilpotent functions at a non-degenerate arc, D. Bourqui, M. Haiech — Manuscripta Mathematica, 2020. Springer
- Non-Complete Completions, M. Haiech — in Arc Schemes and Singularities, World Sci. Publ., 2020. World Scientific
See also my CV for a complete list of my research activities.
Teaching
CRYPTIS Master — University of Limoges
I teach Computer Algebra, Polynomial Systems and Applied Algebra (algebraic attacks via Gröbner bases). The master CRYPTIS trains students in cryptology, security and post-quantum topics.
2024–2025
- OSAB1 — Statistical tools applied to biology (L1)
- Advanced Algebra (L2) — logic, polynomials, groups, rings, roots of unity
- Mathematics PPPE (L1)
- Computer Algebra (M1 CRYPTIS) — polynomial/matrix multiplication, factorizations, etc.
- Polynomial Systems (M1) — resultants and Gröbner bases
- Applied Algebra (M2 CRYPTIS) — algebraic attacks via Gröbner bases
- Python (L1 SAE) — Python basics
- Python (L1 SAE) — advanced basics (recursion, dicts, classes)
2023–2024
- OSAB1 — Statistical tools applied to biology (L1)
- Advanced Algebra (L2) — logic, polynomials, groups, rings, roots of unity
- Mathematics PPPE (L1)
- Computer Algebra (M1 CRYPTIS) — labs: polynomial/matrix multiplication, factorizations, etc.
- Polynomial Systems (M1) — labs on resultants and Gröbner bases
- Applied Algebra (M2 CRYPTIS) — algebraic attacks via Gröbner bases
- Python (L1 SAE) — Python basics
2022–2023
Responsibilities: Head of the PPPE Bachelor track (preparatory pathway for primary-school teachers). Info: official page.
- OSAB1 — Statistical tools applied to biology (L1)
- Advanced Algebra (L2)
- Mathematics PPPE (L1, L2)
- Computer Algebra (M1 CRYPTIS)
- Polynomial Systems (M1)
- Applied Algebra (M2 CRYPTIS)
Supervision
PhD thesis
-
Romaric Neuveu — 2023–ongoing
Topic: "Study of square spaces for the design of a cryptographic signature protocol",
Co-supervised with Philippe Gaborit
Master 1
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Iscia Kasperek — M1 CRYPTIS, Limoges, 2025
Topic: "Isogeny-based cryptography",
Co-supervised with Tristan Vaccon
Bachelor
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Charlie Bordas — L2 Mathematics, Limoges, 2025
Topic: "Introduction to cryptography and hash functions (MD5)"
-
Hector Bouton — L3 ENS Ulm, 2022
Topic: "Fast computation of tropical determinants over p-adics",
Co-supervised with Tristan Vaccon
Other
Internships
- Directed reading (L3, 2015) with Aude Le Gluher, supervised by Julien Sebag — Bézout’s Theorem.
- L3 internship (2015), supervised by Fabrice Orgogozo, CMLS, École Polytechnique — Galois theory and reduction mod p.
- M1 internship (2016), supervised by François Loeser, IMJ-PRG — Model theory.