I heard that the following theorem is proved recently by Foreman-Magidor, which answers a famous old open question:

Theorem.It is consistent, relative to the existence of large cardinals, that there is a singular strong limit cardinal $\kappa,$ such that the tree property hold at both $\kappa^+$ and $\kappa^{++}.$

Here are some questions related to the above theorem:

1) Does anyone know the main idea of the proof?

2) Is the $\kappa$ in the theorem large, or it can be also small, like $\aleph_\omega?$

3) What kind of large cardinal(s) are used in the proof?

4) Are there any notes or slides presenting the proof (as far as I know the paper itself is not written yet, as I asked Magidor for the paper, and did not receive anything).