Minkowski Bases of Type Cones in Deformation Theory

Watch a 55-minute lecture from the IPAM Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop where Federico Castillo explores the concept of deformation cones in fan structures and their relationship to polytope spaces. Delve into the mathematical challenge of finding bases for these cones, particularly focusing on collections of polytopes that can uniquely represent elements through signed sums. Examine a systematic methodology for constructing bases within barycentric subdivisions of simplicial fans, with specific attention to the braid fan and normal fan of simplex products. Learn about indecomposable polytopes and their significance in basis construction, drawing from collaborative research with Spencer Backman at the Pontificia Universidad Católica de Chile.