We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial improvements to the best known lower bounds on the communication complexity of a large class of permutation functions in the 3-player Number-on-Forehead model. Underpinning both ... more >>>

We initiate the study of the *randomness complexity* of differential privacy, i.e., how many random bits an algorithm needs in order to generate accurate differentially private releases. As a test case, we focus on the task of releasing the results of $d$ counting queries, or equivalently all one-way marginals on ... more >>>

Trevisan and Vadhan (FOCS 2000) introduced the notion of (seedless) extractors for samplable distributions as a possible solution to the problem of extracting random keys for cryptographic protocols from weak sources of randomness.
They showed that under a very strong complexity theoretic assumption, there exists a constant $\alpha>0$ such that ... more >>>