Évènements

Spatial Λ-Fleming Viot processes, or SLFVs, are a family of models describing the evolution of genetic diversity for populations living in a spatial continuum. Their main characteristic is their « event-based » reproduction dynamics, which makes it possible to control local reproduction rates. Therefore, they are particularly suited to the study of populations living in unbounded regions.
In this talk, I will introduce a family of SLFV processes, called k-parent SLFVs, which were developed to model spatially expanding populations. I will present what is currently known of the growth properties of the occupied area in k-parent SLFVs. Of particular interest is the growth dynamics of the limiting process when k→ +∞, which is reminiscent of continuous first-passage percolation but has distinct growth features. I will conclude with preliminary results obtained on the genetic diversity at the front edge.
Based on a joint work with Amandine Véber (MAP5, Univ. Paris Cité) and Matt Roberts (Univ. Bath).

Le système d’Euler-Korteweg (compressible) est une perturbation dispersive des équations d’Euler modélisant les effets de la capillarité. Il peut se voir comme une équation de Schrödinger quasilinéaire dégénéré, et dans certains cas particuliers, est équivalent à l’équation de Schrödinger non linéaire via un changement de variable, la transformation de Madelung.
On discutera dans cet exposé de quelques résultats sur la dynamique des solutions que cette analogie laisse espérer (soliton, scattering, limite « semi classique »), certains étant maintenant des théorèmes.