My research interests intersect mathematics and computer science. In particular, I am interested in the following topics:
- Algebraic methods in linear rewriting:
- Commutative and noncommutative Gröbner bases.
- Completion algorithms.
- Lattice structures and rewriting theory.
- Representations of rewriting systems by reduction operators.
- Constructive methods in algebra:
- Effective homological algebra.
- Formal methods for dynamical systems.
- Symbolic computation and applications to module and operad theories.
- Quotients of the magmatic operad: lattice structures and convergent rewrite systems, with Christophe Cordero and Samuele Giraudo, Experimental Mathematics, to appear, arXiv:1809.05083.
- 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.
- A geometric stabilization of planar switched systems, with Rosane Ushirobira and Giorgio Valmorbida , submitted to IFAC World Congress (IFAC 2020), hal-02366928, 2019.
- Normal forms of matrix words for stability analysis of discrete-time switched linear systems, with Laurentiu Hetel and Rosane Ushirobira, submitted to European Control Conference (ECC 2020), hal-02069712, 2019.
- A constructive version of Warfield's Theorem, hal-02120656, 2019.
- Topological rewriting systems applied to standard bases and syntactic algebras, submitted to Journal of Algebra, arXiv:1907.06394, 2019.
- The diamond Lemma for non-terminating rewriting systems using deterministic reduction strategies, with Maxime Lucas, 8th International Workshop on Confluence (IWC 2019), Dortmund, June 2019.
- The diamond Lemma for free modules, 7th International Workshop on Confluence (IWC 2018), Oxford, July 2018.
- Generalizations of the associative operad and convergent rewrite systems, with Christophe Cordero and Samuele Giraudo, 4th Workshop Higher-Dimensional Rewriting and Algebra (HDRA 2018), Oxford, July 2018.
- Detecting useless critical pairs, 6th International Workshop on Confluence (IWC 2017), Oxford, September 2017.
- Upper-bound of reduction operators and computation of syzygies, 3rd Workshop Higher-Dimensional Rewriting and Applications (HDRA 2017), Oxford, September 2017.
- An algebraic approach to confluence and completion, 5th International Workshop on Confluence (IWC 2016), Obergurgl, September 2016.
- Reduction operators: rewriting properties and completion, 2nd Workshop Higher-Dimensional Rewriting and Applications (HDRA 2016), Porto, June 2017.
- Confluence algebras and acyclicity of the Koszul complex, Workshop Higher-Dimensional Rewriting and Applications (HDRA 2015), Warsaw, June 2015.
Thesis and implementation of reduction operators