Interpolation tensor categories

Tensor categories, that is, loosely speaking, categories with two operations ⊕ and ⊗, lie at the heart of modern representation theory, various areas of algebra, and mathematical physics. A class of tensor categories of recent interest consists of so-called interpolation categories, whose study was initiated by Pierre Deligne. An interpolation category can usually be defined in three equivalent ways: representation theoretically via a family of algebraic objects, like the collection of all symmetric groups; categorically as a universal tensor category subject to specific conditions; and combinatorially via a graphical calculus involving string diagrams.


In the first part of the talk, I will explain this trinity of definitions and give a gentle introduction to interpolation categories. In the second part, I will explain some of my research on the structure of interpolation categories and their monoidal centers, including joint work with N. Harman, R. Laugwitz, and S. Posur.