We address a classical mystery of developmental biology : how does a cell in an organ know what overall size the organ has ? According to the current paradigm, the Drosophila wing disc grows robustly to the right size because its cells respond to both signalling proteins (morphogens) and mechanical stress. Due to the long-range nature and directional dependence (anisotropy) of stress, we hypothesize that size regulation can be achieved if cells respond exclusively or primarily to stress. To test this, we develop a morpho-elastic continuum mechanical model of the wing disc in which tissue stretching stimulates cell proliferation, whereas compression inhibits it. Our model relies on the local coupling of growth and the deviatoric (traceless) part of the stress tensor, as well as a homeostatic pressure. The predictions of our model are consistent with a number of experimental observations : the spatial uniformity of cell proliferation in the wing disc, a buildup of compression in the disc center and tension in the periphery during development, and a sigmoidal evolution of the disc size which approaches a final size. To ensure that the same final size is reached even if initial conditions are perturbed, we show that the addition of a basal growth term is necessary, producing a robust encoding of the final size. Our results suggest that local mechanical feedback, which previously was assigned at most a supporting role in size regulation, may be the primary mechanism in obtaining the final disc size.

We consider a time-dependent two-level quantum system interacting with a free Boson reservoir. The coupling is energy conserving and depends slowly on time, as does the system Hamiltonian, with a common adiabatic parameter ε. Assuming that the system and reservoir are initially decoupled, with the reservoir in equilibrium at temperature T ≥ 0, we compute the transition probability from one eigenstate of the two-level system to the other eigenstate as a function of time, in the regime of small ε and small coupling constant λ. We analyse the deviation from the adiabatic transition probability obtained in absence of the reservoir. Joint work with Marco Merkli and Dominique Spehner

In this talk I will present a work in progress related to the analysis of a Bose-Einstein condensate with three-body interactions. Roughly speaking, in an ultra cold gas of Bosons most particles share the same one-body quantum state. The accuracy of this picture depends on how much particles interact with one another. In this setting, particles see each other only if they are at least three in the same neighbourhood. We are interested in the Gross-Pitaevskii regime, where the mean-field approximation (i.i.d variables) does not hold anymore and the correlations do contribute to leading order. I will first review the usual two-body interaction case and then discuss the trivial and non-trivial extensions to the three-body case.

We propose a definition of `minimal symmetry breaking’ of the cosmological principle. By Bianchi’s classification of all Lie algebras of Killing vectors on 3-spaces this minimal symmetry breaking allows for only three examples : the axial Bianchi I, V and IX universes. We show that the latter two are incompatible with the Einstein equations for dust.

La métrique de De Sitter-Reissner-Nordström est une solution de type trou noir aux équations d’Einstein-Maxwell. L’équation chargée de Klein-Gordon sur cette métrique est alors une équation hyperbolique superradiante (i.e. il n’existe pas d’énergie conservée positive).
En supposant le produit de la charge du trou noir avec la charge du champ scalaire suffisamment petit devant la masse du champ scalaire, nous pouvons montrer la décroissance de l’énergie locale des solutions de l’équation à l’aide d’une expansion en termes de résonances du propagateur, ainsi que l’existence et la complétude des opérateurs d’onde associés à l’équation (dont l’interprétation géométrique est possible dans un espace-temps de dimension supérieure).
Les propriétés de décroissance et de diffusion des champs classiques sont des prérequis importants pour construire une théorie quantique des champs en espace-temps courbe.