Update on Hironaka's Proof.
As I wrote a few days ago, Hironaka claimed to have obtained a proof of resolution of singularities in characteristic p > 0. Today he completed his series of six talks.
As expected, pretty early in the series things began to go above my head. But I diligently sat through all the talks. Talking to some experts after the talks, I was given the impression that this proof, or a very precise program of a proof, is extremely promising. It is expected to work. Hironaka promised to write up the remaining part in the future which is expected to outline all the ingredients of the proof.
I guess people will be eagerly looking forward for that future publication by Hironaka.