Research interests

My research interests intersect mathematics and computer science. In particular, I am interested in the following topics:

• Linear rewriting: (non)commutative Gröbner bases, completion procedures, lattice structures and rewriting theory, representation of rewriting systems by reduction operators.
• Effective algebra: constructive homological algebra, formal methods for functional systems, symbolic computation and applications to module and operad theories.

Journal papers

• Confluence of algebraic rewriting systems, with Benjamin Dupont and Philippe Malbos, Mathematical Structures in Computer Science, 32(7): 870-897, 2022.
• Quotients of the magmatic operad: lattice structures and convergent rewrite systems, with Christophe Cordero and Samuele Giraudo, Experimental Mathematics, 30(4): 513-530, 2021.
• Topological rewriting systems applied to standard bases and syntactic algebras, Journal of Algebra, 550: 410-431, 2020.
• A lattice formulation of the noncommutative F4 procedure, International Journal of Algebra and Computation, 29(1): 23-40, 2019.
• Syzygies among reduction operators, Journal of Pure and Applied Algebra, 223(2): 721-737, 2019.
• Reduction operators and completion of rewriting systems, Journal of Symbolic Computation, 84: 57-83, 2018.
• Confluence algebras and acyclicity of the Koszul complex, Algebras and Representation Theory, 19(3): 679-711, 2016.

Conference papers

• Computation of Koszul homology and application to involutivity of partial differential systems, with Thomas Cluzeau and Alban Quadrat, IFAC Symposium on System Structure and Control (SSSC 2022), hal-03908688.
• Compatible rewriting of noncommutative polynomials for proving operator identities, with Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger, International Symposium on Symbolic and Algebraic Computation (ISSAC 2020), arXiv:2002.03626.
• A geometric stabilization of planar switched systems, with Rosane Ushirobira and Giorgio Valmorbida, IFAC World Congress (IFAC 2020), hal-02366928.
• Normal forms of matrix words for stability analysis of discrete-time switched linear systems, with Laurentiu Hetel and Rosane Ushirobira, European Control Conference (ECC 2020), hal-02069712.

Thesis

Le treillis des opérateurs de réduction : applications aux bases de Gröbner non commutatives et en algèbre homologique (in french), defended in December 2016, Paris Diderot University.

Preprints

• Topological closure of formal power series ideals and application to topological rewriting theory, with Thomas Cluzeau and Adya Musson-Leymarie, arXiv:2402.05511 (under revision).
• Strategies for linear rewriting systems: link with parallel rewriting and involutive divisions, with Maxime Lucas, arXiv:2005.05764.
• Presenting isomorphic finitely presented modules by equivalent matrices: a constructive approach, with Thomas Cluzeau and Alban Quadrat, hal-02501322.
• A constructive version of Warfield's Theorem, hal-02120656.