Markus Reineke: Dimension expanders and quiver representations

We will briefly review some ideas and results from the representation theory of quivers.

We then relate the notion of dimension expanders to quiver representations, and use results on so-called general subrepresentations to derive optimal expansion coefficients.

Building on this, we propose a general definition of expander representations of quivers as a qualitative refinement of so-called slope stability, and prove existence of uniform expander representations for any wild quiver.