About

I am a post-doctoral researcher interested in the numerical study of a variety of problems arising from physics. Before joining TUM, I was a PhD student and then a temporary researcher at the Université de Bourgogne in Dijon, France.

I am currently working in the implementation of efficient techniques to determine approximate solutions of a class of high-dimensional time-dependent PDEs. In particular, solutions that can be constructed as the sum of a finite number of time-dependent Gaussians.

Previously, I worked on a numerical approach to the Schottky problem, which consists in determining whether a given g×g complex symmetric matrix with positive definite imaginary part is defined by a Riemann surface of genus g. Then I moved to the study of axially symmetric spacetimes constructed on a class of hyperelliptic curves; part of my work focused on setting up tools to compute geodesics in an efficient manner in order to visualize these non-trivial spacetimes.
The common factor in these works is the theta function, which is a series whose summands are Gaussians. 

Publications

• E. B. de Leon, J. Frauendiener, C. Klein. Computational approach to the Schottky problem. 2023. (Accepted: Special issue AMS). Preprint: arxiv.org/abs/2303.15249v1
• E. B. de Leon. On a class of solutions to the Ernst equation. 2024. (Accepted: Math. Res. Letters). Preprint: arxiv.org/abs/2310.19095
• E. B. de Leon, J. Frauendiener, C. Klein. Visualisation of counter-rotating dust disks using ray tracing methods. Class. Quantum Grav. 41 155005 (2024)

• E. B. de Leon, C. Klein, D. Korotkin. Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods. 2025. (Accepted: Physical Review D). Preprint: arxiv.org/abs/2501.04509