Branching Brownian motion is a model in which independent particles move as Brownian motions and branch at rate 1. Its behavior, and in particular the description of what happens near its extremal particles (the ones furthest away from the origin) is by now well understood in
dimension 1. By contrast, not much is known about the multidimensional case.

In this talk I will present the first step towards the goal of obtaining the limiting extremal point process for the branching Brownian motion in
higher dimensions. This involves in particular finding an analogue of the so-called derivative martingale, which plays a crucial role in d=1,
and studying its convergence.

Based on a joint work with Bastien Mallein (Université Paris 13).