Équipe CFHP

Ongoing thematics for internships/PhD/projects

The following thematics are ongoing in the team. You are welcome to contact us if you are looking for a internship/project/...

Integro-differential algebra.

The team is specialist in formal manipulations of nonlinear PDE (partial differential equations). We developed algorithms in C ( BLAD) which are useful for solving parameter estimation problems (see this poster for more information).

Recently, we have developed new algorithms to replace differential equations by integral equations [BLLRR16], which are usually more suited numerically. An ongoing challenge is to develop an elimination theory for integro-differential equations. Students already have contributed in that area, and are welcome to join us on this thematic. For more details, you can have a look at [BLRUV17] and [BKLPPRU14]

High performance computing (HPC).

We are currently using HPC for improving Numerical and Symbolic Computations in the following directions:

numerical integration of systems of integro-differential equations [BCCLLPQV18]
fast polynomial evaluation over modular integers (collaboration with Prof. Mike Monogan, Vancouver, Canada)

Fast algorithms for singularities of plane algebraic curves.

One thematic of the team involves the elaboration of fast algorithm to study the local behaviour of singularities of plane algebraic curves. This involves theoretical improvment on the complexity of Puiseux series computation [PR15] and practical consideration (a C implementation of a modular-numeric strategy is currently done). An HPC implementation is strongly considered.

PhD subjects

2025–...

Validated numerical software for algebraic curves with singularities

Internships/projects/...

2024–2025

Selection of previous internships/projects

Mike Petrault (M2 Calcul Scientifique Univ. Lille 2024) worked on the multi-thread parallelization of a code that minimizes biases in galaxy distance measurement catalogs
Arthur Vinciguerra (M2 Informatique ENS Lyon 2024) designed and implemented numerical validated algorithms for Hensel's lifting and approximate roots of bivariate polynomials
Mathieu Leroy (lycéen 1^re 2024) visited our team during one week to discover academic scientific research
Jasmin Krüger (M2 Calcul Scientifique Univ. Lille 2023) designed and implemented numerical validated algorithms for bivariate polynomials: fast inversion, Euclidean division and Hensel's lifting
Bilal El Safah (L3 Informatique Univ. Lille 2023) translated to Julia and improved a Fortran code that minimizes biases in galaxy distance measurement catalogs
Léo Soudant (L3 Informatique ENS Paris–Saclay 2022) worked on validated numerical routines for multiple root-finding of univariate polynomials
Louis Gaillard (L3 Informatique ENS Lyon 2021) formalized rigorous Fourier approximations in Coq and a fixed-point a posteriori validation routine for algebraic functions
Louis Roussel (GIS5 Polytech'Nantes 2022) who worked on computing Integral Equations using Machine Learning
Ambroise Fleury (L3 2018 - Accélération SIMD d'évaluations de polynômes) who achieved a 10x speedup on polynomial evalution
Joseph Lallemand (ENS Cachan - 2014) who contributed to [BLLRR16]

Alumni

Arthur Vinciguerra (M2 2024), Mathieu Leroy (lycéen 1^re 2024), Jasmin Krüger (M2 2023), Bilal El Safah (L3 2023), Léo Soudant (ENS Paris 2022), Louis Roussel (GIS3 Polytech'Nantes 2020 GIS5 Polytech'Nantes 2022), Clément Monnier (M2 2021), Louis Gaillard (L3 2021), Gaoussou Sissoko et Clément Richefort (GIS3 Polytech'Lille 2019), Ryan Lefebvre (M2 Mocad 2019), Mellila Bouam (2019), Ambroise Fleury (L3 2018 and M1 PJI 2019), Guillaume Maitrot (M2 2018).