Recorded 13 February 2025. Anastasia Chavez of Saint Mary's College of California presents "The valuation polytope on height two posets" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: Geissinger defined the valuation polytope as the set of all [0,1] -valuations on a finite distributive lattice. Dobbertin showed the valuation polytope is equivalently defined as the convex hull of vertices characterized by all the chains of a given poset. In this project, we study the valuation polytope, VAL(P) , arising from a poset P of height two on n elements. We consider height two posets, generally, and the zig-zag poset and complete bipartite poset, specifically. We will present results on normalized volumes, the existence of unimodular triangulations, and f -vectors. An important ingredient is an associated graphical matroid which we highlight throughout the talk. This is joint work with Federico Ardila, Jessica De Silva, Jose Luis Herrera Bravo, and Andr\'{e}s R. Vindas-Mel\'{e}ndez. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/