Recorded 11 February 2025. Bennet Goeckner of the University of San Diego presents "Vertex order shellings" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: Shellings are ubiquitous tools in the study of simplicial complexes, and the existence of a shelling implies strong topological, algebraic, and combinatorial properties for a complex. In this talk, we consider shellings induced by the order of the vertices of a complex. A classic theorem of Björner in this vein states that a pure simplicial complex is a matroid independence complex if and only if every order on its vertices induces a shelling. We consider complexes defined via various vertex order conditions and determine which of these vertex orders induce shellings. Joint with Marta Pavelka. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/