An exponential improvement for Ramsey lower bounds

I've only skimmed the paper, but this looks very nice: the construction is very simple (aside from the precise choices of the parameters), just the analysis to show that it works is difficult.

(I bet the construction can be refined - it feels like there is a semidefinite programming problem lurking in the background, so there is probably a way to mindlessly optimize things with an SDP solver once the proof technique is rephrased a bit.)