Julie Bergner

Title: Approaches to (∞,n)-categories
Abstract:  The structure of an (∞,n)-category, or homotopical higher category, has become important not only in category theory and abstract homotopy theory, but is also arising in a number of other areas of mathematics, including topology, mathematical physics, and algebraic geometry.  In this talk, we’ll start with the idea of what an (∞,n)-category should be, and why we might want to consider such structures.  Then we will consider ways to model them by explicit mathematical objects, and why it is good to do so in different ways.  We will focus on small values of n but give an indication of how these models can be generalized to higher n.