Communication complexity of XOR functions $f (x \oplus y)$ has attracted increasing attention in recent years, because of its connections to Fourier analysis, and its exhibition of exponential separations between classical and quantum communication complexities of total functions.However, the complexity of certain basic functions still seems elusive especially in the ... more >>>

We show that if one can solve 3SUM on a set of size $n$
in time $n^{1+\epsilon}$ then one can list $t$ triangles in a
graph with $m$ edges in time $\tilde
O(m^{1+\epsilon}t^{1/3+\epsilon'})$ for any $\epsilon' > 0$. This is a
reversal of Patrascu's reduction from 3SUM to
listing triangles ... more >>>

We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem and deviate significantly from known Fourier-based methods, which require the underlying distribution to have some product ... more >>>