We study depth three arithmetic circuits with bounded top fanin. We give the first deterministic polynomial time blackbox identity test for depth three circuits with bounded top fanin over the field of rational numbers, thus resolving a question posed by Klivans and Spielman (STOC 2001).

Our main technical result is ... more >>>

Let \mathcal{F} = \{F_1, \ldots, F_m\} be a finite set of irreducible homogeneous multivariate polynomials of degree at most 3 such that F_i does not divide F_j for i\neq j.
We say that \mathcal{F} is a cubic radical Sylvester-Gallai configuration if for any two distinct F_i,F_j there exists a ... more >>>