Given two disjoint semialgebraic subsets of a given compact semialgebraic set, we describe an algorithm that certifies that the two subsets are disconnected, i.e. that there is no continuous path connecting them. The certificate of disconnectedness is a polynomial satisfying specific positivity conditions. It is computed by solving a hierarchy of convex moment-sum-of-squares semidefinite programs.

This is joint work with Mohab Safey El Din.