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It is well known that if $V: \mathbb{R}^n \to \mathbb{R}$ is a uniformly convexÌýpotential then the measure whose density with respect to the LebesgueÌýmeasure on $\mathbb{R}^n$ is $e^{-V}$, satisfies several concentration propertiesÌý(such as a PoincaréÌýinequality and the fact that Lipschitz functions haveÌýa sub-Gaussian tail). In this talk, we try to find analogs of this fact whenÌý$\mathbb{R}^n$ is replaced by the Boolean hypercube, hence, the density $e^{-V}$ isÌýwith respect to the uniform measure on the Boolean hypercube. In this case,Ìýit is not clear what should be the correct definition of log-concavity, andÌýeven when $V$ is quadratic (which is trivial in the Gaussian case), provingÌýconcentration becomes a challenging question (with implications toÌýspin-glasses, for example). We'll present two results in this direction:ÌýFirst, we will suggest a natural definition of log-concavity which attainsÌýsuch concentration, namely, in terms of the (semi) log-concavity of theÌýmultilinear extension. Second, we will present a result which givesÌýsufficient conditions for concentration of quadratic forms, and inÌýparticular implies that the Gibbs measure on the Sherrington-KirkpatrickÌýmodel admits concentration when the temperature is higher than someÌýuniversal constant. Based on joint works with Koehler, Shamir and Zeitouni.