The talk presents a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, one obtains a monotonicity testing algorithm that makes n^{1/2} non-adaptive queries to a function f:{0,1}^n -> {0,1}, always accepts a monotone function and rejects a function that is far from being monotone with constant probability.

Joint work with Dor Minzer and Muli Safra.