Abstract:

The problem of classifying modular categories is motivated by applications to topological quantum computation as algebraic models for topological phases of matter. These categories have also applications in different areas of mathematics like topological quantum field theory, von Neumann algebras, representation theory, and others. In this talk, we will start by introducing some of the basic definitions and properties of fusion, braided, and modular categories, and we will also give some concrete examples to have a better understanding of their structures. We will empathize some of the interesting properties that modular categories carry with them. We will give a brief overview on the situation of the classification program for this kind of categories.

( This talk is in the room APM 7218)

  Abstract:

In this talk we will investigate some topological properties of the space Fk(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of the configuration spaces Fk(M) to become increasingly complicated. Church and others showed, however, that when M is a connected and open, there is a representation-theoretic sense in which these configuration spaces stabilize. In this talk I will explain these stability patterns, and how they generalize classical notions of homological stability proved by McDuff and Segal in the 1970s. I will describe higher-order "secondary stability" phenomena established in recent work joint with Jeremy Miller. The project is inspired by work of Galatius--Kupers--Randal-Williams.

(It is a joint algebra and topology seminar.)

( This talk is in the room APM 7421)