An introduction to quiver moduli

In the last fifty years quiver representations have been increasingly used in various fields of mathematics, from representation theory to topological data analysis, to algebraic geometry.

In this talk, we will give an introduction to the theory of their moduli spaces and to several topics of active research within it.

We will construct these moduli spaces using King's geometric invariant theory and overview their relation with the representation theoretical properties of quivers.

Several parallels with the geometry of moduli of vector bundles on algebraic curves will be drawn, both showcasing analogous results and similar steps in their proofs.

Time permitting, we will describe several aspects of the geometry of these quiver moduli, such as their deformation theory, their birational properties, and the description of their derived categories.

This work is supported by the Luxembourg National Research Fund (FNR-17953441).