Routing problems in computer science often involve computing efficient routes for moving entities between different points in some defined space. Given a semi-ring $R$ and a graph $G$, the Algebraic Path Problem provides a unifying framework for analyzing various routing problems mathematically by abstracting the notion of combining weighted paths on $G$ under the additive operation defined on $R$. Routing problems defined on planar graphs are fairly understood, but these same problems remain elusive when defined on more-complex topological structures. In this talk, I will discuss current work that utilizes sheaf cohomology to understand the nature of routing problems defined on cellular complexes. In so doing, we will find a nice generalization of the Algebraic Path Problem. This is joint work with Russell Funk and Thomas Gebhart.

My talk slides can be found on my webpage (kswillingham.net) as well as at the following link: https://drive.google.com/file/d/1lY9Wn9A3VHGXwUjA0Oe0B1MkydOaAIIT/view?usp=drive_link