A Noisy Interpolating Set (NIS) for degree $d$ polynomials is a
set $S \subseteq \F^n$, where $\F$ is a finite field, such that
any degree $d$ polynomial $q \in \F[x_1,\ldots,x_n]$ can be
efficiently interpolated from its values on $S$, even if an
adversary corrupts a constant fraction of the values. ... more >>>

We show that disjointness requires randomized communication
Omega(\frac{n^{1/2k}}{(k-1)2^{k-1}2^{2^{k-1}}})
in the general k-party number-on-the-forehead model of complexity.
The previous best lower bound was Omega(\frac{log n}{k-1}). By
results of Beame, Pitassi, and Segerlind, this implies
2^{n^{Omega(1)}} lower bounds on the size of tree-like Lovasz-Schrijver
proof systems needed to refute certain unsatisfiable ... more >>>

We extend the 'Generalized Discrepancy' technique suggested by Sherstov to the `Number on the Forehead' model of multiparty communication. This allows us to prove strong lower bounds of n^{\Omega(1)} on the communication needed by k players to compute the Disjointness function, provided $k$ is a constant. In general, our method ... more >>>