Polynomial Maps With Noisy Input-Distributions

A problem from theoretical computer science posed by Buhrman asks to show that a certain class of circuits (NC0[+]) is bad at decoding error correcting codes under random noise. (This would be in contrast with an analogous class of quantum circuits.) These circuits can be modeled by constant-degree polynomial maps, which turns out to make the problem amenable to a structure-versus-randomness analysis based on a new notion of rank for polynomial maps. In this talk I will aim to discuss a solution to Buhrman's problem along these lines as well as connections with other notions of rank for polynomials and tensors. Based on joint work with Davi Castro-Silva