Jan 29. 2026, 14:30 — 15:00

We provide an asymptotic analysis of a nonlinear integro-differential equation which describes the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is modeled via a nonlinear integral term, known as the  Fisher's  infinitesimal model. Considering a small variance regime, we characterize the steady states of the problem and we analyze their stability. Our method relies on a spectral analysis involving Hermite polynomials, highlighting the specific structure of the nonlinear reproduction term. This is a joint work with M. Hillairet.