Recorded 10 February 2025. Anton Dochtermann of Texas State University - San Marcos presents "Interval complexes, linear resolutions, and spaces of digraph maps" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: We study ideals generated by the (complements of) facets of d-dimensional "interval" simplicial complexes. This class recovers interval graphs when d=1, and strictly contains the class of pure shifted complexes. They also played a role in recent work of Benedetti, Seccia, and Varbaro in their study of determinantal facet ideals. We construct minimal cellular resolutions of such ideals, supported on a certain space of directed graph homomorphisms that generalize the "box of complexes resolutions" of Nagel and Reiner. We conclude that these ideals have linear resolutions, providing a generalization/specialization of Froberg's theorem regarding edge ideals of chordal graphs. Based on old joint work with Alex Engstrom, as well as more recent conversations with Bennet Goeckner and Marta Pavelka. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/