Contemporary environmental challenges, such as climate change, the depletion of natural resources, ecosystem degradation, and the energy transition, require increasingly sophisticated tools for analysis and forecasting. In this context, mathematics plays a central role by providing models, methods, and theoretical frameworks that make it possible to study complex systems, analyze large-scale data, and propose sustainable management strategies.

This lecture will present various mathematical approaches applied to environmental sciences, including modeling, the study of partial differential equations, numerical analysis, and scientific computing. Drawing on recent examples from interdisciplinary collaborations, we will discuss both the contributions and the limitations of mathematical tools when faced with uncertainty and the complexity of environmental phenomena. This reflection aims to highlight the role of mathematics as a common language between disciplines and as a decision-making tool for environmental policies.

The meeting will in particular address the following topics:

1. Mathematical modeling of natural processes: oceanic and atmospheric dynamics, pollutant diffusion, wildfire propagation, and water resource management.

2. Diffusion equations: modeling the spread of pollutants in the air, soil, and oceans.

3. Navier–Stokes equations: understanding atmospheric and oceanic movements, which are essential for climate prediction.

4. Elasticity equations: describing the deformation of the Earth's crust, with direct applications in volcanology to understand magma ascent, anticipate eruptions, and assess associated risks.

5. Wave equations: simulating the propagation of seismic waves, tsunamis, or vibrations in complex natural media.

6. Inverse problems with applications to climatology, the identification of natural disasters, and the detection of pollution sources.

Through concrete examples, the lecture will demonstrate how the combination of mathematical theory and computational power contributes to the development of forecasting, optimization, and sustainable management tools in service of the environment.

Thomas Alazard (Ecole Normale Supérieure, Paris-Saclay)
Romain Briandet (Université Paris-Saclay, AgroParisTech)
Cosmin Burtea (Université paris cité)
Valérie Cayol (Université Clermont Auvergne)
Siyu Cen (Université de Rouen Normandie)
Carlotta Donadello (Université de Franche-Comté)
Nuutti Hyvönen (Université de Aalto, Finlande)
Youcef Mammeri (Université Jean Monnet)
Lisl Weynans (Université de Bordeaux)