E_\infty-structure and differentials of the Adams spectral sequence

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive formulas for the differentials. It is based on the A∞-structures [2], E∞-structures [3], [4], [5], [6] and functional homology operations [7], [8], [9]. This approach will be applied to the Kervaire invariant problem [10], [11].