His work on the zig-zag product, with Omer Reingold and Avi Wigderson, was awarded the 2009 Gödel Prize.

Crucial to the intuition and simple analysis of the properties of the zig-zag product is the view of expanders as functions that act as "entropy wave" propagators—they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated.

A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends (poly)logarithmically on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high min-entropy sources.

These high min-entropy extractors have several interesting applications, including the first constant-degree explicit expanders that beat the "eigenvalue bound."

With Lu, Omer Reingold, and Avi Wigderson, he gave the first construction of randomness extractors that are "optimal up to constant factors," reaching a milestone in a decade of work on the subject.