Hierarchies of contact manifolds via rational SFT

I will explain the construction of a functor from the exact symplectic cobordism category to a totally ordered set, which measures the complexity of the contact structure. Those invariants are derived from a bi-Lie infinity formalism of the rational SFT and a partial construction of the rational SFT. In this talk, I will focus on the construction and properties of the functor. Time permitting, I will explain applications, computations, and relations to the involutive bi-Lie infinity formalism of the full SFT. This is joint work with Agustin Moreno.