Job offer

European Commission; France; Sur place; EUR 28 000 - 35 000; Plein temps

Résumé du poste

Un projet de doctorat au sein de l'Institut Montpelliérain Alexander Grothendieck se concentre sur le développement théorique et pratique de modèles mathématiques impliquant des systèmes prédateur-proie. Les candidats doivent détenir un Master en analyse des PDE et posséder des compétences en programmation, notamment en Python, avec un intérêt pour la modélisation biologique.

Qualifications

• Master en équations aux dérivées partielles (PDE) exigé.
• Solides compétences en LaTeX et Python.
• Intérêt pour les modèles biologiques et les systèmes dynamiques.

Responsabilités

• Études théoriques sur des modèles prédateur-proie.
• Développement de schémas numériques et implémentation.
• Dissemination des résultats via publications et conférences.

Connaissances

Analyse des équations aux dérivées partielles

Compétences numériques

LaTeX

Python

Intérêt pour les modèles biologiques

Systèmes dynamiques

Formation

Master en analyse des équations aux dérivées partielles

Description du poste

Organisation/Company CNRS Department Institut Montpelliérain Alexander Grothendieck Research Field Mathematics History » History of science Researcher Profile First Stage Researcher (R1) Country France Application Deadline 10 Jul 2025 - 23:59 (UTC) Type of Contract Temporary Job Status Full-time Hours Per Week 35 Offer Starting Date 1 Oct 2025 Is the job funded through the EU Research Framework Programme? Not funded by a EU programme Is the Job related to staff position within a Research Infrastructure? No

Offer Description

This project will be funded by the DyGéSTE program of the IMPT for a period of three years, with additional support for research resources. It will be developed at the Institut Montpelliérain Alexander Grothendieck.

The research may also include in-depth theoretical studies on lesser-explored equations, focusing on the existence of solutions, Turing instability analysis, and convergence of numerical schemes. These aspects could lead to collaborations with research teams in Toulouse (Ariane Trescases, Sepideh Mirrahimi) and Paris (Ayman Moussa, Laurent Desvillettes).

This PhD project aims to achieve both theoretical advances and practical applications. It will focus on the study of predator-prey models involving interactions between otters, crayfish, and trout, through systems of ordinary differential equations (ODEs) and partial differential equations (PDEs).
The initial mathematical objective is to compile a comprehensive set of relevant equations, along with a review of the current state of knowledge: existence of theoretical solutions (well-posedness), development of numerical schemes, and their implementation in one-dimensional and two-dimensional domains, as well as on graph structures.
Special attention will be given to cross-diffusion systems, particularly to prey-taxis type models. This thesis will contribute both methodologically and in terms of applied research to the modeling of spatial dynamics in predator-prey systems.
The results will help converge toward one or more models and associated equations that are consistent with empirical data from CEFE (Centre d'Écologie Fonctionnelle et Évolutive). We also plan to disseminate the findings through publications in academic journals and presentations at national and international conferences.

Master's degree in partial differential equations (PDE) analysis, with a strong theoretical background in the field and solid skills in numerical tools, particularly LaTeX and the Python programming language. An interest in biological models and dynamical systems is also expected.