Thanks to Irit Dinur for telling me about the following:
Oded Goldreich’s recent choice is about the paper: Circuit Lower Bounds for Nondeterministic Quasi-Polytime: An Easy Witness Lemma for NP and NQP, by Corry Murray and Ryan Williams.
(ACC stands for Boolean functions that can be described by bounded depth polynomial size citcuits with Boolean gates and mod 6 gates.)
Oded’s next choice is a paper by Roei Tell pointing out a remarkable direct consequence from the Murray-Williams result for the hardness vs. randomness agenda.
If the goal is to show that BPP=P implies that NP ≠ P, then if earlier we had results 10% this strong the consequence is perhaps 70% strong.
Remarks: Above there are links to three posts (by Oded, Scott, and Dick and Ken) on Ryan’s older result. I wrote several posts on bounded depth circuits of several kinds, here (with an interesting comment by Ryan!), here, here, and here.
Update: Here is a detailed blog post over GLL about the breakthrough