# Critical branching diffusions in bounded domains.

I will discuss branching diffusions in a bounded domain D in which particles are killed upon hitting the boundary. It is known that any such process undergoes a phase transition when the branching rate reaches a critical value: the first eigenvalue of the generator of the diffusion. I will consider various properties of the critical system, including the structure of the associated genealogical tree. When the system is conditioned to survive for a long time, it turns out that this tree converges to the Brownian CRT .