Russell Impagliazzo, Cris Moore, and Alex Russell just posted their new proof of the sharp form of the “Level 1 Inequality” (AKA Talagrand’s Lemma, AKA Chang’s Lemma). It’s completely beautiful, and basically 3 lines long. What’s doubly cool is that they pretty much came up with it on the spot during a lecture on the topic at Denis Thérien’s 2012 Barbados workshop.
Speaking of which, Li-Yang Tan heroically scribed those Barbados lectures and did a terrific job. You can find the resulting notes on analysis of boolean functions here.
Finally, the open problems in analysis of boolean functions, compiled at the Simons Symposium, have been arXived. Daniel Kane even solved one of them in the meantime!