Maths For the Earth

Remark: You are brillant student interested in a M2 Research Internship followed by a PhD thesis in Applied Maths mixing modelization and mathematical analysis related to complex flows encountoured in environmental challenges. Do not hesitate to send me an email. We can define together a subject of mathematics in possible interactions with other disciplines.

ARP MathsInTerre: Being particularly interested in the impact of mathematics and computer science in natural and human sciences,  with Emilie Neveu, I have coordinated a Think-tank project during the year 2013. The ‘MathsInTerre’ Research Think-tank was a project financed by the French National Research Agency (ANR), with the aim of making a contribution to a morfe systemic and integrated vision of the subject “Mathematics and the complexity of the Earth system”. Its ultimate goal was to stimulate discussion upstream of the definition of an action plan for the ANR.
Comparisons between French and other research systems are also made.

All the results and reports are available on

This ARP MathsInTerre has been the first stone to build the Mathematical Institute for Planet Earth. Mathematics is a fundamental discipline which is at the heart of important issues related to the complexity of the earth and more particularly to the environment. Understanding both research and suitanable management problems on this subject requires the adaptation of mathematical techniques in interaction with  other disciplines which have links with fluids, living and human. Conversely, environmental issues can also allow the development of new mathematical theories, which in turn can provide a better understanding of the complexity of phenomena studied for decision support. Following a recommendation of its CSI (Scientific Council INSMI), based on the document of the ARP MathsInTerre mentionned above, the INSMI-CNRS supports the creation of a national Institute of Mathematics for the Planet Earth and this has been written page 17 in the COP document (Objectives and performance contract between the French state and the CNRS). A. Guillin was appointed project manager within INSMI for the implementation of this important structure and for a starting implementation through the Federation Auvergne-Rhône-Alpes with my help based on the material obtained during the ARP MathsInTerre. As a first step,  the CNRS (under the impulsion of the INSMI and the participation of INSU, INEE, INP) has created in May 2021 the Mathematical Intitute of Planet Earth hosted at ENS Lyon in partnership and financially supported with the ENS Lyon and the universities Clermont-Auvergne, Grenoble-Alpes, Claude Bernard Lyon 1, Jean-Monnet Saint-Etienne and Savoie Mont Blanc. Recurring sources of funding are more than necessary to support such national (even international) collaborative tool on a long-term. These financial supports could come from public institutions but also from private sponsors. People, universities, institutions or private compagny who are interested to know more on the project and/or are interested to financially support the Mathematical Institute of Planet Earth could contact Arnaud Guillin ( at the University Clermont-Auvergne, France. The leadership of this institute is ensured by Laure Saint-Raymond with Arnaud Guillin as excutive director with a real interdisciplinary scientific committee:  That’s a great news. I am part of the executive office of the Mathematical Institute of Planet Earth with F. Bouchet, S. Speich, W. Thuiller, A. Veber including Laure Saint-Raymond and Arnaud Guillin. A multidisciplinary scientific committee has also been set up constituted as follows:

Living Earth : Sylvie Méléard (Random-Biology-Medicine, Polytechnique), Vincent Cal-
vez (PDE-Biology, Lyon 1), Patricia Reynaud-Bouret (Statistic-Medicine, LJAD), Arezki
Boudaoud (Plant Morphogenesis, Orsay), Jérome Chave (biodiversity, Bordeaux), Jocelyn
Chanussot (INPG, Grenoble).

Human Earth: Bertrand Maury (systems of particules and collective motions, Orsay – INSMI), S. Sorin (game theory, Sorbonne U.), Gaël Giraud (Economy, AFD), Denis Couvet (Ecological transition, Museum), Céline Guivarch (Energies, Ec. Ponts), Didier Roux (Académie des Technologies).

Solid/fluid earth: David Lannes (Costal and offshore flows and wave-structure interaction, IMB –INSMI), Eric Blayo (Ocean-Atmophere coupling, UGA), Josselin Garnier (Earth and propagation of waves, Polytechnique), Jean-Noêl Thépaut (climate, CEPMMT), Jean Jouzel (Climate and ice, Académie des sciences), Sandrine Bony (Clouds, atmosphere and climate, EMC3 Paris), S. Morin (Mountain and climate, CNRM, Météo-France).

Note that the executive office of IMPT has organized the first school on morphological impacts of climate change  in Lyon (23-26 November 2021) and has organized also public events with musée des confluences (26-27 November 2021) under the subject: « face au changement climatique, le champ de possibles. » In particular, see the conference by H. Le Treut and the round table by I. Chuine, C. Guivarch and H. Le Treut.

An example of an interdisciplinary research project: An ERC Synergy project (submitted in November 2019 by F. Bouchut (maths-numerics), A. Mangeney (geophysics), F. Radjai (mechanics) and myself (math-theory)) relies on synergistic interactions of four PIs at the crossroads of granular mechanics, mathematical analysis, design of numerical methods and geophysics.  The ambition is to develop a game-changing modeling strategy that will provide unprecedented clues for extracting key landslide characteristics (geometry, composition, and dynamics) from recorded waves. A SlideWaves laboratory creation is also proposed in this project. Our ERC Synergy project has been retained in the first step (november 2019) and in the second step (June 2020) of the scientific evaluations. The final step with a web-conference interview with the evaluation panel took place in the begining of september with the four PIs. Unfortunately this ERC project (71/441) has not been retained for funding due to the small number of projects that has been selected (34/441). We have submitted the november 2021 a new version thanks to a hard joint synergistic work between all of us and the communicative pugnacity of Anne and Farhang in the redaction as well as the complicity acquired by a collaborative work for years between Anne and François. I’m really excited by this project which contains scientific fundamental questions with a focus on a real environmental problem. Our ERC Synergy project has been retained in the first step and in the second step of the scientific evaluations. The final step with an interview in Brussels with the evaluation panel has taken place in the begining of september 2022 with the four PIs. Unfortunately we have received a negative answer in October 2022.

An example of an interdisciplinary working group: With C. Lacave (Institut Fourier – Grenoble),  L. Saint-Raymond (UMPA ENS Lyon) and A. Venaille (Lab Phys ENS Lyon), we have been organizing a monthly interdisciplinary working group at UMPA ENS-Lyon since 2017 called MathsInFluids related to oceanography. This working group aims to promote exchanges within mathematics (by mixing deterministic and probabilistic approaches, continuous and discrete approaches), but also between mathematicians and physicists (by crossing experiments and theoretical approaches).

15 years between two important events 2004 and 2019…..

In 2004, I coorganized with J. Videman and J.M. Urbano part of a CIM Thematic Term  on mathematics and the environment in Lisboa intending to promote the interdisciplinary aspects of Environmental Sciences, emphasizing the role of modern applied mathematics in the modeling and the analysis of complex natural phenomena.

In 2019, A.–L. Dalibard coorganized with M. Ghil,  S. Speich and H. Le Treut a Thematic Semester  at IHP aiming to explore the Climate System and the developments in mathematics that seem most promising in advancing the climate and environmental sciences.

Researchers are really interested to promote multi-disciplinary interactions for planet earth with mathematics but it misses efficient scientific and financial tools to create a real dynamic in this direction with mathematics (theory AND numerics) to face climate challenges.  15 years between these two important events without real ambitious national and international research programs involving mathematics and disciplines related to planet earth, the time that has passed cannot be recovered…….Hopefully, it seems to change: The idea of the mathematical Institute for planet earth and the proposition of the slidewaves laboratory for the ERC synergy project go in that direction (see above).

An interesting initiative — Mathematics of Planet Earth Webinars : A series of weekly webinars to give the opportunity to ECRs, PhD students and Post-Docs, working on topics related to Mathematics of Planet Earth, to share their work with researchers at ALL levels in the field. Two contributions of 30 minutes + 10 minutes discussion each on the following topics:

  1. PDEs and SPDEs in fluid-dynamics;
  2. Numerical models for fluid-dynamics;
  3. Dynamical systems: critical transitions and linear response in the Earth system;
  4. Data analysis methods for climate records.

A list of interdisciplinary collaborations with mathematics. People interested by a list of interdisciplinary collaborations are referred to this link. Mathematicians who are interested to appear on this web-page may contact myself with a short description of the questions arising from other disciplines, their interdisciplinary collaboration and the explanation of the mathematics (theory and numerics) which are involved.

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