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). Applications towards automatic (time delay systems) is an ongoing work [BPQ16]

PhD subjects

Two subjects are available (the availabilty of the PhD fundings will depend on the quality of the students and administrative decisions)

Internships/projects/...

2019-2020:

Selection of previous internships/projects

Alumni

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).