Real Galois cohomology of simply connected groups by the example of E_7

By the celebrated Hasse principle of Kneser, Harder and Chernousov,
calculating Galois cohomology  H^1(K,G)  of a simply connected simple
algebraic K-group G over a number field K reduces to calculating
H^1(R,G) over the field of real numbers R.  For some cases, in
particular, for the split
simply connected R-group G of type E_7, the first calculations of
H^1(R,G)  appeared only in 2013 and 2014 in preprints of Jeffry Adams,
of Brian Conrad, and of the speaker and Zachi Evenor. All these
calculations used the speaker's note of 1988.

In the talk I will explain the method of Kac diagrams of calculating
the Galois cohomology set H^1(R,G)  for a simply connected simple
algebraic R-group G by the examples of groups of type E_7. The talk is
based on a work in progress with
Dmitry A. Timashev. No preliminary knowledge of Galois cohomology or
of groups of type E_7 is assumed.