Inflation and the factory of primordial black-holes

Gravitational wave astronomy has opened a new window to test the population of black-holes in the universe. The origin of these BHs is still an open question. If the majority of BHs are produced in the early universe, they could constitute a fraction of the dark matter or act as seed for supermassive BHs. Taking this as a motivation, I will discuss how to produce primordial BHs during inflation. In particular, I will focus on single-field models where PBHs arise from a second plateau in the potential. I will show that in these models quantum diffusion plays an important role, impacting the estimation of the abundance of PBHs.