Integrable connections

Abstract: Definition of curvature and integrable connection. Statement of the equivalence between the category of local systems and the category of vector bundles with integrable connection. Variants: schemes, relative setting.

Reference: Deligne, 2.10 to the end of Section 2; Conrad, Classical motivation for the Riemann-Hilbert correspondence. Notes from the talk are attached under "slides".

algebraic geometrynumber theory

Audience: advanced learners

( slides )

---

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

---