Recorded 12 February 2025. Martina Juhnke of the Universität Osnabrück presents "Algebra, Geometry and Combinatorics of Cosmological polytopes" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: Arkani-Hamed, Benincasa and Postnikov defined a cosmological polytope associated to a Feynman diagram in their study of the cosmological flat space wavefunctions. Each such polytope contributes to this wavefunction via its canonical form. The theory of positive geometries tells us that one way to compute this canonical form is as a sum of the canonical forms of the facets of a triangulation of the polytope. In this talk, we will discuss an algebraic approach to this theory: We show that the toric ideal of every cosmological polytope has a squarefree Gröbner basis. The corresponding triangulation can be described purely combinatorially via certain decorated graphs. This enables us to also derive the h*-polynomial and the normalized volume for special classes of graphs via half-open decompositions. This is based on joint work with Justus Bruckamp, Lina Goltermann, Erik Landin, Liam Solus and Lorenzo Venturello. If time permits, I will also hint at some beautiful (yet not well understood) connections to Physics, involving graph tubings and differential equations satisfied by the flat space wavefunction, which is ongoing work with Daniel Baumann, Claudia Fevola and Harry Goodhew. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/