Graduate Seminar

Location:  CL 305

Speaker: Aditya Dwarkesh

PhD Student supervised by Francis Bischoff

Title: Surface signatures

 Abstract:

The path signature is a way to encode a path on a space in terms of a noncommutative power series. This is done through the machinery of connections on the space. The path signature is the parallel transport of a certain ‘universal’ connection on the space which is valued in a free Lie algebra.

We will introduce a higher-dimensional generalization of it known as the surface signature. This is defined by considering higher connections valued in a Lie 2-algebra. It turns out that the universal 2-connection is also intimately related to the basic gerbe, which is an example of a ‘categorified’ principal bundle. In this talk, we will bring these concepts together.