Astrometric weak lensing from Dark Matter substructures

It has been recently pointed out that variable weak gravitational lensing effects on the motion of background stars can be used to probe nonluminous structures inside the Milky Way halo. I will describe one possible detection strategy targeting collapsed dark matter structures in the mass range from million to billion solar masses. The data analysis technique will be discussed in detail with an application to the second data release of Gaia.