Algebra, Geometry and Combinatorics of Cosmological Polytopes

Explore a 49-minute lecture from the Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop at UCLA's Institute for Pure & Applied Mathematics, where Professor Martina Juhnke from Universität Osnabrück delves into the mathematical foundations of cosmological polytopes. Discover how these geometric structures, first introduced by Arkani-Hamed, Benincasa, and Postnikov, contribute to cosmological flat space wavefunctions through their canonical forms. Learn about the groundbreaking algebraic approach that demonstrates how every cosmological polytope's toric ideal possesses a squarefree Gröbner basis, and understand how these triangulations can be described using decorated graphs. Gain insights into the calculation of h*-polynomials and normalized volumes for specific graph classes through half-open decompositions. Explore fascinating connections between physics and mathematics, including graph tubings and differential equations related to flat space wavefunctions, based on collaborative research with Daniel Baumann, Claudia Fevola, and Harry Goodhew.