This project focuses on various aspects of branching processes in fixed, variable or random environments, whether they are single-type or multitype. We propose to identify the limit of Bienaymé-Galton-Watson trees conditioned by their total population through their coding by multi-indexed and matrix-valued random walks. Then we will study the problem of the extinction of a part of the population for continuous multitype branching processes. We will construct the continuous analogue of multitype Bienaymé-Galton-Watson trees. These continuous random trees will then be obtained in the stable case as scaling limits of the renormalized discrete trees. These continuous random trees will be associated with continuous multi-type branching processes. We will also study discrete-time multitype branching processes in random environments to obtain asymptotic properties of the corresponding population size and survival probability; in particular, the problems of large deviations and asymptotic normalization will be considered. To this end, we will first deepen the study of the products of random matrices, in particular through the study of the multidimensional processes corresponding to the linear action of these products of matrices. We will be particularly interested in the cases where these processes are conditioned to remain in a cone of the Euclidean space. We will then establish limit theorems (invariance principle, local limit theorem, ...) for these conditioned processes. We will finally focus on the fundamental branching martingale associated to these Bienaymé-Galton-Watson trees, defined from the corresponding products of random matrices.

The VR-MARS project represents a support system for urgent healthcare delivery in isolated environments, based on virtual reality and embodied conversational agents (ECA). We hypothesize that these two technologies enable better situational awareness and care coordination between 3 parties: a care provider in an isolated location, a critically ill patient and the control centre on Earth. VR-MARS explore the scientific fields of emergency medicine, human factors and virtual reality. The use case of VR-MARS will be related to space medicine, in particular emergency care during a manned spaceflight to Mars. During these missions, temporal isolation will add to physical isolation, because of delays in communication between the care provider (on Mars) and ground control (on Earth), which will preclude real-time telemedical support. VR-MARS will be built around two simultaneous decision loops which will allow task assignment and synchronisation between the care provider, the ECA and ground control. The ECA will interact with the care provider via augmented reality. Upon request, it will deliver step-by-step guidance on medical protocols, using reassuring verbal tone and cues in order to mitigate the stress of the care providers. As soon as it is available, ground control on Earth will be made aware of the situation on Mars and of the procedures being undertaken by the care provider. This will improve situational awareness on the ground and enable the most optimal decision making in the mid- to long-term. In return, ground control will deliver its recommendation to the care provider via the ECA. Therefore, the ECA will represent the central hub of communication between the two sites. VR-MARS will be tested on two medical scenarios involving a critically ill patient represented by a high-fidelity simulator. Technical and non-technical skills of the care provider will be assessed at two levels: immediate interactions between the care provider and the ECA (for urgent, life-saving decisions) and delayed interactions between the care provider and ground control (for mid- and long-term decisions). With regards to research output and spinoffs, we anticipate that VR-MARS will improve medical care in remote environments, such as humanitarian missions, the combat environment, medical evacuations, expedition medicine, etc.

Malnutrition, which includes extreme hunger, undernutrition and obesity among other conditions, affects a large part of the human population, especially in the intertropical zone. In the Pacific, a significant part of the food comes from coral reef fisheries. The nutritional quality of fish (e.g. macro- and micro-nutrients) is an essential element of the nutritional health of local populations. However, various risks affect fish communities, such as pollution by contaminants, habitat degradation, etc. In this context, the TONIC project has 3 objectives. The 1st will assess the nutritional quality of fish consumed by local populations. The 2nd will evaluate the experimental effects of 2 major pollutants on the nutritional value, survival and fecundity of 2 fish species, frequently consumed by human local populations. The 3rd will model different scenarios (increase in temperature and pollution, overfishing, etc.) on the nutritional quality of fish. This will allow looking at the 'balance' between risks and benefits associated with fish consumption and to inform decision-markers.

Energetic particles are ubiquitous in magnetically confined fusion plasmas. They contain a significant fraction of the plasma energy and are thus vital for the performance of fusion devices such as ITER. However, the presence of energetic particles and the fact that fusion plasmas are complex systems heated up to hundred million degrees result in instabilities that reduce the confinement of energetic particles. Understanding, predicting and controlling their transport and losses is of prime importance and constitutes our main goal. This is a high-dimensional multi-scale nonlinear problem, for which a complete description is so far unaffordable. Therefore, we propose a novel and inter-disciplinary approach to develop numerical tools based on Artificial Intelligence techniques applied to two lines of research: (1) derive data-driven reduced models for transport of energetic particles and (2) optimize the information extracted from HPC gyro-kinetic simulations and from experiments.

The purpose of this project is to push forward the development of asymptotic analysis in General Relativity in 4 essential directions. 1. Scattering on non stationary backgrounds; conformal scattering. Scattering theory is a precise tool of analysis of the asymptotic behaviour of fields, giving such information as asymptotic propagation speed, local decay of energy, equivalence between the field and its asymptotic profiles. It has been developed to considerable refinement using spectral analysis, but is not at present adapted to non self-adjoint cases or time-dependent situations. Our purpose is to extend the theory in both directions. First we propose to study the Klein paradox and superradiance on the Kerr metric (a phenomenon by which bosons can extract energy from the black hole) using spectral techniques. Second, we wish to develop an alternative approach to scattering based on Penrose's conformal compactification. It has already been applied successfully to non stationary situations in trivial topology. We mean to extend its range of validity to allow for the presence of black holes and give a different treatment of superradiance. 2. Quantum fields. The Hawking effect predicts the emission of a thermal radiation by a collapsing star and is in a way a quantum analogue of the famous no-hair theorem, since the thermal radiation is characterized only by the mass, charge and angular momentum of the resulting black hole. The first mathematically rigorous descriptions of this effect have been obtained recently and in some idealized situations: only free fields are considered; the proofs rely heavily on the detailed structure and high symmetry of the black hole background and on the details of the simplified collapse models considered. Our main goal is to go beyond these idealizations by considering perturbations of the metric, by taking the interior of the star into account, and -- more ambitiously still -- by going beyond the free field theory. The importance of these questions is clear in view of the expected universality of the Hawking effect. Linked to the Hawking effect is the simpler Unruh effect according to which a uniformly accelerated detector in Minkowski space-time ``sees'' a thermal radiation when coupled to a quantum field in its vacuum state. The rigorous study of the behaviour of detectors coupled to quantum fields around eternal or collapsing black holes is another goal of this project. 3. Stability. A fundamental question in relativity is the stability of universe models. This is a problem of paramount difficulty and only solved sofar for the flat empty universe. But one expects that as in the flat case, the behaviour of the full system is driven by that of the linearized one. The question of linear stability is therefore crucial and is also more tractable. It amounts to studying hyperbolic partial differential equations on a fixed background and understanding their stability and decay properties. We shall investigate the decay of fields for various values of the spin on a Kerr background or small perturbations of it. Brane cosmologies, related to the AdS/CFT correspondence conjecture, will also be considered, in view of developing scattering theories for non linear equations of quantum field theory on brane universes. 4. Inverse scattering. A scattering theory and the associated distribution of resonances encode part of the geometry of the background metric. The inverse scattering programme initiated recently aims at working out how much geometric information can be recovered from the knowledge of the scattering matrix or the distribution of resonances on a black hole spacetime. This is a physically natural question with direct applications to the interpretation of data from gravitational wave detectors, especially for resonances which are expected to be the measurable quantities. We shall consider inverse scattering at fixed energy and the inverse resonance problem for De Sitter-Kerr-Newman black holes.