Since 2016 I have been a PhD student in the group of László Erdős at the Institute of Science and Technology Austria. My research interests are probability theory and mathematical physics with a focus on random matrices. I am also interested in universal properties of complex systems and the mathematically rigorous study of machine learning algorithms.

## Curriculum vitae

• 2010 – 2011. BSc, ETH Zurich
• 2011 – 2014. BSc and MSc, LMU Munich
• 2014 – 2015. MASt, University of Cambridge, Clare College
• 2015 – 2019. PhD, IST Austria
• 04 – 08/2018. Industry Sabbatical, Bosch Center for Artificial Intelligence
• from 10/2019. Junior Fellow, Institute for Theoretical Studies, ETH Zurich

Curriculum vitae (pdf) for more detailed information.

## Theses

• PhD Thesis From Dyson to Pearcey: Universal Statistics in Random Matrix Theory for a PhD in Mathematics supervised by László Erdős
• MSc Thesis Phase Transition in the Density of States of Quantum Spin Glasses for the MSc in Theoretical and Mathematical Physics supervised by László Erdős
• Essay Interlacing Families and the Kadison–Singer Problem for the Master of Advanced Studies in Mathematics supervised by Timothy Gowers
• BSc Thesis Integrated Density of States of Random Schrödinger Operators with Alloy-Type Potential for the BSc in Mathematics supervised by Peter Müller

## Publications

All my publications can be found on the arXiv, on Google Scholar and on the MathSciNet.

1. Phase Transition in the Density of States of Quantum Spin Glasses
with László Erdős (2014)
Math. Phys. Anal. Geom. 17 (2014), no. 3-4, 441–464.
arXiv:1407.1552, MR3291938, doi:10.1007/s11040-014-9164-3

2. Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues
with László Erdős (2016)
Int. Math. Res. Not. IMRN 2018, no. 10, 3255–3298.
arXiv:1608.05163, MR3805203, doi:10.1093/imrn/rnw330

3. Fluctuations of Functions of Wigner Matrices
with László Erdős (2016)
Electron. Commun. Probab. Volume 21 (2016), paper no. 86, 15 pp.
arXiv:1610.07084, MR3600514, doi:10.1214/16-ECP38

4. Random Matrices with Slow Correlation Decay
with László Erdős and Torben Krüger (2017)
Forum of Mathematics, Sigma, 7, E8 (2019).
arXiv:1705.10661, MR3941370, doi:10.1017/fms.2019.2

5. Correlated Random Matrices: Band Rigidity and Edge Universality
with Johannes Alt, László Erdős and Torben Krüger (2018)
accepted for publication in Ann. Probab.
arXiv:1804.07744

6. Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
with László Erdős and Torben Krüger (2018)
submitted
arXiv:1809.03971

7. Cusp Universality for Random Matrices II: The Real Symmetric Case
with Giorgio Cipolloni, László Erdős and Torben Krüger (2018)
accepted for publication in Pure Appl. Anal.
arXiv:1811.04055

8. Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
with Giorgio Cipolloni and László Erdős (2019)
preprint
arXiv:1908.01653

9. Edge Universality for non-Hermitian Random Matrices
with Giorgio Cipolloni and László Erdős (2019)
preprint
arXiv:1908.00969

## Research Rotations

1. Limits to gene regulation due to crosstalk.
with Gašper Tkačik
Internal report (2015)
2. Analysing response of retinal neurons in fish and Generalization bounds for active task selection.
with Christoph Lampert
Internal report (2016)

## Contact Information

• Email dschroed[at]ist.ac.at
• Phone +43 2243 9000 7485
• Office I21.O3.106 (Lab Building West, 3rd floor)