### Thibault Poiret

University of St Andrews

Thursday 21 September 2023, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

** Limit line bundles and metric graphs **

Given a space X, geometers often care about understanding vector bundles on X,
i.e. "nice continuous maps E -> X such that the preimage of each point is a vector
space". When the vector spaces have dimension 1, these are called line bundles.
Line bundles on compact smooth curves (compact curves that look like a line from up
close) have very nice properties. However, limits of smooth curves tend to acquire
singularities and line bundles on singular curves are much more ill-behaved. We will
talk about how, in the singular case, one can use combinatorics on metric graphs to
recover some version of the nice properties enjoyed by the smooth case.

series: Pure Mathematics Colloquium

organiser: Scott Harper