Proof of the Riemann-Hilbert Correspondence

Abstract: After a quick review of the key concepts we learned before, I will present the statement and a sketch of the proof of the Riemann-Hilbert correspondence; namely, the equivalence of categories between algebraic vector bundles with regular integrable connections and holomorphic vector bundles with an integrable connection on a complex algebraic variety (and its analytification, respectively). After that, I will also present a simple example to illustrate why we should have the regularity condition imposed on the algebraic side. We will follow Chapter II Section 5 of Deligne.

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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