Multivalued functions, and abstract derivations and connections

Abstract: Our next goal is to study extensions of vector bundles and connections on an open (non-compact) surfaces. In this talk, we introduce relevant concepts and their basic properties. We first generalize the idea of multivalued functions to sheaves and show its relations to monodromy representations. We also introduce and study the valuations of a function under the action of a connection.

Deligne, Sections I.6 and the beginning of II.1.

algebraic geometrynumber theory

Audience: advanced learners

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.