Algebraic Graph Theory - John S. Caughman

Monday, September 11, 2023 11:30 am - 11:30 am EDT (GMT -04:00)

Title: Parameter constraints for distance-regular graphs that afford spin models

Speaker: John S. Caughman
Affiliation: Portland State University
Location: Please contactSabrina Latofor Zoom link

Abstract: In 1990, Vaughn Jones introduced a link invariant constructed using matrices known as spin models. In 1996, Francois Jaeger discovered that spin model matrices are contained in the Bose-Mesner algebra of an association scheme. Since many examples of association schemes arise from distance-regular graphs, it is natural to ask which distance-regular graphs afford a spin model. Several known families exist, and it is conjectured that the known list is complete. In this talk we present results describing the Terwilliger algebra of a distanceregular graph Γ that affords a spin model. We use the results to restrict the possible parameters of Γ. In future work, we expect that such restrictions could lead to a classification of the distance-regular graphs that afford a spin model.