**Title:** Connections in algebraic geometry

**Abstract:**

Any tangent category has a notion of connection for its differential bundles (the analog of vector bundles). In this talk, we’ll explore what this definition gives us in the tangent category of affine schemes. The talk will be roughly divided into three parts: (1) connections in general, and how they are described in a tangent category, (2) a review of the tangent category of affine schemes, (3) some particular examples of connections in the tangent category of affine schemes, and how the abstract tangent categorical definition relates to existing definitions of connections in algebraic geometry.

This talk will be split into two parts. The first part starts at 10am, the second one at 11:30am

The speaker’s notes on algebraic geometry can be found at https://www.reluctantm.com/gcruttw/publications/alg_geo_notes.pdf