I will describe the essential ideas of using Dirac ensembles to describe random (quantum) geometries. Using connections with random matrix theory we are able to study various properties of these Dirac ensembles. In particular I will show how the addition of a fermion changes some of these properties. I will also discuss the direction I hope to take this research in the future.

Bio: Luuk Verhoeven obtained his Ph.D. in 2023 working with Prof. Masoud Khalkhali. His current research focusses on single-matrix Dirac ensembles with the aim to understand the (quantum) geometries these Dirac ensembles describe. Previous work includes describing immersions of smooth manifolds in the language of spectral triples and unbounded products.