קולוקוויום בביה"ס למדעי המחשב - New forms of hypercontractivity, with applications
The classical hypercontractive inequality for the Boolean hypercube lies at the core of many results in analysis of Boolean functions. Though extensions of the inequality to different domains (e.g. the biased hypercube) are known, they are often times quantitatively weak, making them hard to apply. In this survey talk, we will discuss new forms of the hypercontractive inequality. These new forms are quantitatively stronger for the class of "global functions", which are functions in which no small set of variables can change the value of the function with significant probability. We will also discuss some applications to the study of sharp-thresholds, noise sensitivity on the biased hypercube and extremal combinatorics. No special background is assumed. Based on joint works with Peter Keevash, Noam Lifshitz and Eoin Long.