Relationship to PDEs and $n$th order differential equations

Abstract: Via local trivializations of vector bundles and connections, we translate the conditions of horizontal sections and flat connections in terms of classical differential equations. We then associate vector bundles with connections to higher order differential equations and finally prove an equivalence between the categories of these objects (with additional data).

Reference: Deligne, Sections 3 and 4.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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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.

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