Skip to main content
To KTH's start page To KTH's start page

Erik Landin: The cosmological polytope of the complete bipartite graph K_{2,n}

Time: Wed 2023-06-14 10.15 - 10.45

Location: 3418 , Lindstedsvägen 25

Respondent: Erik Landin

Export to calendar


 A cosmological polytope of an undirected connected graph is a lattice polytope which when the graph is interpreted as a Feynman diagram can be used to calculate the contribution of that Feynman diagram to the wavefunction of some cosmological models. This contribution can be calculated using the canonical form of the cosmological polytope, which can be computed by taking the sum of the canonical forms of the facets of a subdivision. Juhnke-Kubitzke, Solus and Venturello showed that the cosmological polytope of any undirected connected graph has a regular unimodular triangulation. They characterized the facets of such triangulations for trees and cycles to yield combinatorial formula for the desired canonical forms. Here we characterize the facets of such a triangulation of the complete bipartite graph $K_{2,n}$ and use that characterization to calculate the normalized volume.