In this series of three talks, we'll investigate how to define and work with the idea of vector fields and their associated flows in the setting of a tangent
category. Tangent categories are categories equipped with an abstract version of the tangent bundle for smooth manifolds; as such, vector fields are easy to define in this setting. However, to talk about their associated flows requires more care: we need
an object "which uniquely solves ordinary differential equations" in the tangent category. We'll investigate this idea, and then focus in particular on how considering tangent categories of vector fields and flows gives us a new perspective on commutation
of vector fields and flows. If time permits, we will also consider flows for linear vector fields in this abstract setting.
This is based on joint work with Robin Cockett, JS Lemay, and Rory Lucyshyn-Wright.
Department of Mathematics & Statistics
6316 Coburg Road
PO BOX 15000
Halifax, Nova Scotia
Canada B3H 4R2