Description du sujet de thèse

Large Random Matrix Theory relies on the fact that regularization occurs in large dimension and one can get a clear picture of many matrix features such as spectral properties and other fine properties. Recent articles have already exploited these properties in the context of theoretical ecology.

The aim of this study is to apply this theory to a context of adaptive dynamics and quantitative genetics, in order to understand the evolutionary dynamics of large-scale ecological systems.

The study of biodiversity dynamics necessarily relies on an understanding of its biological evolution. At present, most theoretical models concerned with the evolution of species traits are restricted to a small number of traits in a small number of species. This project aims to extend this framework by using the theory of large random matrices to make generic predictions about the evolution of large ecological systems. Such predictions will make it possible, for example, to understand under what conditions the diversification of living organisms may tend to accelerate (“diversity begets diversity”), or on the contrary whether certain more or less general conditions maintain strong constraints on the total diversity of an ecological system.


The two advisors François MASSOL and Jamal NAJIM work together since 2018 and have already supervised the PhD thesis of Maxime Clenet (defence in 2022). They have also gathered an interdisciplinary team (mathematics, physics, ecology) to work on questions related to large random matrices in theoretical ecology (involving Mylène Maida, Walid Hachem, Jeff Arnoldi, Matthieu Barbier, Viet Chi Tran, Imane Akjouj and Maxime Clenet).

The current PhD thesis will beneficiate of this expertise.

The applicant should have a strong background in applied mathematics and probability (master level) and a background in mathematical biology/theoretical ecology (at least at a introductory level)

A detailed version of the subject is available hereafter

https://drive.google.com/file/d/1hanzHz6VHvQhBignEZeXOhktYUnLb60e/view?usp=sharing

Contexte de travail

The Ph-D thesis will take place at the "Laboratoire d'Informatique Gaspard Monge" (LIGM, UMR 8049), at Gustave Eiffel university, near Marne La Vallée (suburb train "RER A"- stop at "Noisy Champs").
The two advisors will be François Massol (expert in theoretical ecology) and Jamal Najim (expert in large random matrices).