Recorded 10 February 2025. Federico Castillo of the Pontificia Universidad Católica de Chile presents "Minkowski bases of type cones" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: The deformation cone of a fan, broadly speaking, represents the space of polytopes with the given fan as their normal fan. A basic question is to find a basis—a collection of polytopes such that every element in the deformation cone can be uniquely expressed as a signed sum of these basis elements. Ideally, this basis should consist of indecomposable polytopes, those that cannot be trivially decomposed into a sum of two other polytopes. While such bases are generally difficult to construct, this talk introduces a systematic approach for identifying bases in the context of barycentric subdivisions of simplicial fans. Notable examples include the barycentric subdivision of the braid fan and also of the normal fan of products of simplices. This is joint work with Spencer Backman. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/