Abstract: The cover time is the time needed for the Wiener sausage of radius 1 to cover the torus of linear size n. In dimension $d \geq 3$, A. Sznitman introduced random interlacements to describe the local covering picture at a fixed intensity; They still give a good account at large densities, bridging up to cover time. In dimension 2, with S. Popov and M. Vachkovskaia, we construct random interlacements to describe the neighborhood of an unvisited site at times proportional to the cover time. In this talk, I will explain the Brownian case. (Joint works with Serguei Popov and Marina Vachkovskaia.)