Interval Complexes, Linear Resolutions, and Spaces of Digraph Maps

Explore a 40-minute lecture from Texas State University's Anton Dochtermann at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop, where he delves into the study of ideals generated by facets of d-dimensional interval simplicial complexes. Learn how these structures extend beyond interval graphs and pure shifted complexes, and discover their connection to recent work on determinantal facet ideals. Examine the construction of minimal cellular resolutions supported by directed graph homomorphisms, which build upon Nagel and Reiner's box of complexes resolutions. Understand how these findings lead to linear resolutions, advancing Froberg's theorem on edge ideals of chordal graphs. Based on collaborative research with Alex Engstrom and discussions with Bennet Goeckner and Marta Pavelka, this 2025 presentation at UCLA's Institute for Pure & Applied Mathematics offers deep insights into the intersection of algebra, combinatorics, and discrete geometry.