Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the famous works of Kalyanasundaram-Schnitger and Razborov in 1992. However, the question of obtaining tight bounds for ... more >>>

Proving lower bounds against depth-$2$ linear threshold circuits (a.k.a. $THR \circ THR$) is one of the frontier questions in complexity theory. Despite tremendous effort, our best lower bounds for $THR \circ THR$ only hold for sub-quadratic number of gates, which was proven a decade ago by Tamaki (ECCC TR16) and ... more >>>

A central goal in average-case complexity is to understand how average-case hardness can be amplified to near-optimal hardness. Classical results such as Yao’s XOR lemma establish this principle for Boolean functions, but these techniques typically apply only to artificially constructed functions, rather than to natural computational problems. In this work, ... more >>>