Benjamin Schröter: Good triangulations and h*-polynomials of cosmological polytopes

Abstract: Cosmological polytopes of graphs are a geometric tool in physics to study wavefunctions for cosmological models whose Feynman diagram is given by a graph $G$.
Since their recent introduction by Arkani-Hamed, Benincasa and Postnikov they found the interest of various mathematicians. In particular by Juhnke, Solus and Venturello who introduced the so called good triangulations to prove that these polytopes have unimodular triangulations. Bruckamp, Goltermann, Juhnke, Landin and Solus used these results to compute the $h^*$-polynomials of cosmological polytopes of multitrees and multicycles as we we have seen a few weeks ago in this seminar.

In this talk we move on with the story. We enumerate all maximal simplices in a good triangulation of any cosmological polytope. Furthermore, we provide a method to turn such a triangulation into a half-open decomposition from which we deduce that the $h^*$-polynomial of a cosmological polytope is a specialization of the Tutte polynomial of $G$.
This settles several open questions and conjectures of Juhnke, Solus and Venturello and Bruckamp et al.