Session B3 - Symbolic Analysis
July 15, 17:00 ~ 17:25 - Room B2
Algebraic certificates of disconnectedness
LAAS-CNRS University of Toulouse, France - email@example.com
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 trajectory 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 obtained by applying infinite-dimensional convex duality on a transport equation satisfied by measures attached to trajectories.
Joint work with Mohab Safey El Din (Université Pierre et Marie Curie, Paris, France).