Georgia Institute of Technology College of Sciences

Given a collection of multivariate polynomials $F, F_1, …F_n$, to determine whether $F$ can be written as $F= \sum G_iF_i$ is an important problem, both in theory and practice. In this talk, I will explain how some problems of this nature, even in 2 or 3 variables, can become interesting and difficult. An unexpected connection to a conjecture on sumsets will be explained. As the time of writing, the conjecture is unsolved by both humans and AIs.