10 février 2021

Elisabetta Brocchieri (Université d'Évry)
Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit

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Résumé : I rigorously prove the passage from a Lotka-Volterra reaction- diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of a starvation driven type. We investigate the linear stability of homogeneous equilibria of those systems and rule out the possibility of Turing instability. Numerical simulations are included which are compatible with the theoretical results.

Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit  Version PDF

Thibault Lefeuvre (IMJ-PRG (Jussieu))
The holonomy inverse problem on Anosov manifolds

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Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

Résumé : On a negatively-curved Riemannian manifold (and more generally on an Anosov manifold i.e. a Riemannian manifold whose geodesic flow is uniformly hyperbolic), the celebrated Burns-Katok conjecture asserts that the marked length spectrum, namely the length of all closed geodesics marked by the free homotopy of the manifold, should determine the metric (up to isometries). In a similar fashion, on an Anosov manifold, given a vector bundle equipped with a (unitary) connection, one can wonder if the data of the holonomy of the connection along closed geodesics (up to conjugacy) determines the connection (up to gauge-equivalence). This is called the holonomy inverse problem and turns out to be a very rich question, as it brings together different fields of mathematics : microlocal analysis, hyperbolic dynamical systems, theory of Pollicott-Ruelle resonances & Kähler geometry. I will review some recent progress that have been achieved on this question. Joint work with Mihajlo Cekić.

The holonomy inverse problem on Anosov manifolds  Version PDF