A small quotient of the big absolute Galois group (joint work with Ido Efrat and J\'{a}n Min\'{a}v{c})

This is a report of a talk given at the Oberwolfach workshop on "cohomology of finite groups: Interactions and applications" which was held during July 25th - July 31st, 2010. It is an announcement of some of the results (with motivation) and their applications from the paper "Quotients of absolute Galois groups which determine the entire Galois cohomology"; see arXiv:0905.1364.