I am a doctoral student in Prof. Dr. Gernot Akemann's group. My research topic is the integrability of non-hermitian random matrix ensembles.
What is that?
Imagine you start with an ensemble of NxN random matrices. You want to analyse the distribution of the eigenvalues (e.g. the density). Write it down as an N-fold integral over the joint probability density of the eigenvalues. Now if you solve all of these integrals, your analysis will be much easier. But solving integrals is hard! And you have N of them! You need to find a clever way to compute the integrals.
And here my research can help you. If your matrix model is one of the models that I am researching, otherwise: Good luck!
Random matrix theory with focus on applications in physics.
Currently I am working with quaternionic non-hermitian random matrices that are an extension of Ginibre's quaternion ensemble.