I am a doctoral student in Prof. 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!}

**Office**: E5-133

**E-mail**: markus.ebke(at)uni-bielefeld.de

**PO Box**: #217 (Room V3-128)

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.
I research ways to find the skew-orthogonal polynomials that are used to solve these ensembles and how to compute their large-N limit.

- September 29 - October 5, 2019: KTH in Stockholm, Sweden. I gave a talk in their Random Matrix Theory Seminar on October 3.
- June 21 - September 5, 2021: KAIST in Daejeon, South Korea. I joined the research group of Prof. Ji Oon Lee.
- August 14 - 22, 2021: KIAS in Seoul, South Korea. I was invited by Seong-Mi Seo and Sung-Soo Byun.

- XIV Brunel-Bielefeld Workshop on RMT, December 14 – 15, 2018, at Brunel University in London. I presented a poster about the results of my master thesis: Cauchy-Transform of Orthogonal Hermite and Laguerre Polynomials in the Complex Plane.
- Seventh Bielefeld-SNU Joint Workshop in Mathematics, February 26 - March 1, 2019, at Center for Interdisciplinary Research in Bielefeld
- Research School Coulomb Gas, Integrability and Painlevé Equations, March 11 - 15, 2019, at CIRM in Marseille
- Summer School Randomness in Physics and Mathematics, August 12 - 24, 2019, at Center for Interdisciplinary Research in Bielefeld
- XV Brunel–Bielefeld Workshop on RMT, December 5 - 7, 2019, at Center for Interdisciplinary Research in Bielefeld. I presented a poster about my research so far: Mehler Formulas and Universality for Skew-Orthogonal Polynomials on the Complex Plane.
- Eighth Bielefeld-SNU joint Workshop in Mathematics, February 24 - 26, 2020, at Center for Interdisciplinary Research in Bielefeld. I gave a talk about my research: Construction of Skew-Orthogonal Polynomials from Orthogonal Polynomials for Quaternionic Non-Hermitian Random Matrices.
- XVI Brunel-Bielefeld Workshop on RMT, December 18 – 19, 2020, online event.
- KIAS Mathematics Seminar, June 18, 2021: Symplectic non-Hermitian random matrices - Skew-orthogonal polynomials and universal scaling limits
- Bielefeld-Melbourne Random Matrix Seminar, July 7, 2021: Symplectic non-Hermitian random matrices - Skew-orthogonal polynomials and universal scaling limits
- IRTG Retreat October 24 - 27, 2021: Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble
- XVII Brunel-Bielefeld Workshop on RMT, December 17 - 18, 2021, online event. I presented a poster on Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble

- (with Gernot Akemann and Iván Parra)
**Skew-Orthogonal Polynomials in the Complex Plane and Their Bergman-Like Kernels**, Communications in Mathematical Physics (2021). https://doi.org/10.1007/s00220-021-04230-8 (preprint: arXiv:2103.12114) - (with Sung-Soo Byun)
**Universal scaling limits of the symplectic elliptic Ginibre ensemble**, arxiv:2108.05541 (preprint) - (with Sung-Soo Byun and Seong-Mi Seo)
**Wronskian structures of planar symplectic ensembles**, arxiv:2110.12196 (preprint)