Triple Massey products in Galois cohomology

The Inverse Galois Problem, asking which groups can be realizable as
Galois groups of fields, is a major problem in Galois theory.
For example the fact that there is no general formula for the roots of
a polynomial of degree five follows from the fact that
the symmetric group S_5, which is not solvable, is realizable as a
Galois group of a field.
Minac and Tan conjectured that if G is the Galois group of a field,
then G has vanishing triple Massey products (to be defined in the lecture).
In the talk I will give some general background on this new property
and its relation to the inverse Galois problem via a work of Dwyer, and try to give a
flavor of my proof of the Minac-Tan conjecture.