Raz proposed a program to prove arithmetic circuit lower bounds through the explicit construction of elusive functions. These are polynomial maps from a low dimensional space to a high dimensional ambient space whose image is contained in no subvariety of low complexity. Here, complexity is prescribed in terms of the ... more >>>

Hyperdeterminants are high dimensional analogues of determinants, associated with tensors of formats generalizing square matrices. First conceived for $2\times 2\times 2$ tensors by Cayley, they were developed in generality by Gelfand, Kapranov and Zelevinsky. Yet, hyperdeterminants in three or more dimensions are long conjectured to be VNP-Hard to compute, akin ... more >>>

We present a new algorithm for solving homogeneous multilinear equations, which are high dimensional generalisations of solving homogeneous linear equations. First, we present a linear time reduction from solving generic homogeneous multilinear equations to computing hyperdeterminants, via a high dimensional Cramer's rule. Hyperdeterminants are generalisations of determinants, associated with tensors ... more >>>