Symmetry reduced Flag-hierarchies

Flag-Algebras, first introduced by Razborov in 2007, remain one of the most powerful tools in extremal combinatorics. Recently, Raymond et al. found a connection to polynomial optimization: We can recover Flag-Sums-of-Squares hierarchies by partially exploiting the symmetries of a polynomial optimization hierarchy. We continue from there, and fully exploit the symmetries in this polynomial setting for two different hierarchies, one focusing on a low number of edges, and another focusing on a low number of vertices of appearing Flags.

The pre-seminar will introduce the basics of SDPs, polynomial optimization, and representation theory of S_n for symmetry reduction.