BRODU Virgile

My PhD focuses on the design of mass-structured individual-based models. I study measure-valued processes in which individuals are characterized by traits (age, mass, etc.). Individual dynamics include a continuous evolution of these traits over time, and random births and deaths. Birth and death rates depend on the individual’s traits, which vary over time.

Mathematically, I study the long-term survival of populations described by the process, and I establish convergence results in large populations toward a deterministic model. My work also involves numerical simulations and attempts of model reduction.

These models assume a specific form for birth, death, and energy gain/loss rates, called allometric, and this is justified by an abundant literature in evolutionary biology. I aim for a better understanding of the nature of these allometric relationships, their significance, and their structuring role in ecosystems.

I am currently working on natural extensions of my PhD work.

During my PhD, I was supervised by Nicolas Champagnat and Coralie Fritsch, with whom I continue to work. I also collaborate with the biologist Sylvain Billiard.

My teaching assignments for the 2025-2026 academic year are as follows:

Lectures/tutorials in PDE/Distributions in 2nd year at ENSEM (graduate).
Lectures/tutorials in Probability/Statistics in 1st year at ENSEM (undergraduate).
Tutorials in Engineering Mathematics in 1st year at ENSEM (undergraduate).
Tutorials in Monte Carlo Methods and Applications to Random Processes in 2nd year at Mines de Nancy (graduate).
Tutorials in Operations Research in 1st year at Mines de Nancy (undergraduate).
Supervision of a 2A project (two graduate students) and a 3A project (one graduate student) at Mines de Nancy.

During the three years of my doctoral studies, I was responsible for tutorials at Mines de Nancy. I supervised tutorials in Numerical Analysis and Optimization, Measure Theory and Probability, and Statistics for Engineering, at an undergraduate level.

I also supervised, in collaboration with Coralie Fritsch, the research program of a student from Mines de Nancy, Antonin Clerc (graduate student).

As part of my doctorate, I obtained the Teaching Label from the IAEM doctoral school (teacher training monitoring, supervision of doctoral students starting their teaching career).

Finally, I supervised a mathematics club at the Jeanne d’Arc high school in Nancy for two years (2022-2024). We participated in the TFJM mathematics tournament and won the national edition. We came second in the European edition.

I was elected as a doctoral students representative to the doctoral school Council, as well as to the CLED Council, from 2023 to 2025.

I am currently Vice-Secretary of the Nancy University Choir, after having served as Treasurer from 2023-2024, and then President from 2024-2025.

CV_Virgile_BRODU

• ‘An individual-based stochastic model reveals strong constraints on allometric relationships with minimal metabolic and ecological assumptions’, joint work with Sylvain Billiard, Nicolas Champagnat and Coralie Fritsch. Submitted to Annals of Applied Probability. Currently in review. ArXiv : https://arxiv.org/abs/2501.12257
• Work in progress: ‘An individual-based stochastic model with variable resources: a tightness result with unbounded growth, birth and death rates’.
• Work in progress with Sylvain Billiard: ‘A mathematical view on allometric relationships’.
• My PhD thesis manuscript: Thesis_Brodu

I have had the NVQ (National Vocational Qualification) for being a baker since 2022. I organize the ‘IECL Probability/Statistics seminar brioche’. Every Thursday from 10:15 to 10:45, this friendly moment brings together the team’s researchers around a pastry or brioche made by one of us.