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Description

In this talk I'll introduce the idea of a tangent category, which can be seen as a minimal categorical setting for differential geometry. I'll discuss a variety of examples, and then focus on how analogs of vector spaces and (affine) connections can be defined in any tangent category. Time-permitting, I'll also briefly describe a few other structures that can be defined in a tangent category, including differential forms and (ordinary) differential equations and their solutions.