Team : PolSys

Contributions to polynomial system solving: Recurrences and Gröbner bases

This habilitation thesis deals with polynomial system solving through Gröbner bases computations. It focuses on the link between multivariate polynomials and linear recurrence relations satisfied by a multi-indexed sequence for computing Gröbner bases.
Our contributions mainly lie on the theoretical and practical aspects on these Gröbner bases computations. First, we present msolve, a new open source C library, for solving polynomial systems using Gröbner bases. Second, we describe new algorithms and complexity estimates for computing Gröbner bases either for a total degree order or the lexicographic one. Then, we present linear algebras-based and polynomial-division-based algorithms for guessing linear recurrences with constant or polynomial coefficients, in generic and structured situations.
Finally, we detail our research project for the forthcoming years on these aspects.

Defence : 09/21/2023 - 14h - Campus Pierre et Marie Curie, salle Jacques Pitrat (25-26/105)

Jury members :

Bernard Mourrain, Directeur de recherche, INRIA & Université Côte d’Azur [rapporteur]
Cordian Riener, Professeur, Universitetet i Tromsø – Norges arktiske universitet [rapporteur]
Gilles Villard, Directeur de recherche, CNRS & École Normale Supérieure de Lyon [rapporteur]
Alin Bostan, Directeur de recherche, INRIA & Université Paris-Saclay (examinateur)
Manuel Kauers, Professeur, Johannes Kepler Universität Linz (examinateur)
Fatemeh Mohammadi, Professeure, Katholieke Universiteit Leuven (examinatrice)
Mohab Safey El Din, Professeur, Sorbonne Université (examinateur)

Current position : - Sorbonne Université

2 PhD graduated 2022