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November 1, 2016 2:30 PM
Presented by : Geoff Cruttwell (Mount Allison)
Topic : Differential equations in tangent categories I
Abstract: Tangent categories provide an axiomatic approach to the tangent bundle, one of the central objects in differential geometry. Working in this axiomatization, a number of further important concepts from differential geometry can be defined. In particular, vector fields, the Lie bracket, vector bundles, connections, and de Rham cohomology are all examples of concepts that can be defined within the axiomatic setting of a tangent category.
However, a number of other important concepts in differential geometry (for example, parallel transport, geodesics, and integrability theorems) rely on being able to solve certain (ordinary) differential equations. It is clear that the tangent category axioms alone are not powerful enough to allow one to "solve differential equations" in this setting. The purpose of this talk is to look at additional axioms to add to a tangent category which would allow one to do this, and to see some of the consequences these axioms would entail. (joint work with Robin Cockett and Rory Lucyshyn-Wright)