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title: Branching Brownian motion with selection abstract: The branching Brownian motion (BBM) can be seen as a system of diffusing and reproducing particles. It can also be regarded as a tree-indexed Brownian motion, thereby joining two fundamental concepts in probability theory: Brownian motion and random trees. In this talk I will present some results obtained in my thesis (arXiv:1210.3500) about a model of one-dimensional BBM with selection, called the N-BBM. In this model, as soon as the number of particles exceeds a (large) given number N, only the N right-most particles are kept (space is drawn horizontally), the others being removed from the system. I will expose some precise estimates on the position of the cloud of particles for large N. More precisely, I show that it converges in law at the time-scale log^3 N to a Lévy process, thereby justifying results obtained by the physicists Brunet, Derrida, Mueller and Munier through PDE methods. I will explain as well how this study contributes to the understanding of the so-called noisy FKPP equation.