Workshop on Topology: Identifying Order in Complex Systems

The notion of complexity appears in many different contexts, including in the theory of computation, but also in topology and geometry. In the context of computational complexity there are also famous open questions about separations of complexity classes such as P and NP. In this talk I will discuss how these notions extend to more abstract mathematical structures such as constructible functions and sheaves, and how the classical questions about seperation of complexity classes reduces to studying the complexity of certain functors. After giving some examples, I will mention a recent attempt in developing a unified theory of complexity from a purely categorical point of view. This last part is joint work with Umut Isik.