Continuing from the discussion of asymptotic cohomology from the previous talk, we shall first demonstrate the vanishing results in the case of amenable groups, implying a result of Kazhdan that amenable groups are uniformly stable. I will then explain how to prove that the second cohomology group vanishes for lattices in semisimple groups. The method is broadly an analogue of the corresponding proof of Monod-Shalom that the second bounded cohomology vanishes for such groups.