Sorin Popa - University of California, Los Angeles (UCLA), Mathematics I will present a result showing that any free cocycle action of a countable amenable group Γ on any II1 factor N can be perturbed by inner automorphisms to a genuine action. Besides containing all amenable groups, this {\it vanishing cohomology} property, called \CalV\CalC, is also closed to free products with amalgamation over finite groups. While no other examples of \CalV\CalC-groups are known, by considering special cocycle actions Γ↷N in the case N=R, N=L(F∞), one can be exclude many groups from being \CalV\CalC. I will also explain a connection between the vanishing cohomology problem and Connes’ Approximate Embedding conjecture.