Paul Martin: Some geometrically defined subcategories of the partition category, and associated representation theory

The partition categories and their associated algebras arise in computational statistical mechanics and in invariant theory and elsewhere. They include many interesting subcategories such as the Brauer categories and the Temperley-Lieb categories. We discuss geometrically defined categories interpolating between these various classical objects (introduced in joint work with Kadar and Yu), and comment on the representation theory of the corresponding algebras.