Schubert coefficients are nonnegative integers that arise in Algebraic Geometry and play a central role in Algebraic Combinatorics. It is a major open problem whether they have a combinatorial interpretation, i.e., they are in #P. In this talk we discuss the closely related problem of the positivity of Schubert coefficients and its interactions with the Hilbert Nullstellensatz. We prove a positive rule for this problem under two standard assumptions.

This is joint work with Igor Pak.