Fabian Lander

he/him

Hello! I'm a PhD student in geometry, groups and dynamics at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. This site contains some of my code and writing. The rest is stuck in drafts.

Interactive

Online Demos

Code

Software

Billiards

High-performance C++ simulation of symplectic billiards (on up to two tables) and of the "fourth billiards" dynamical system, whose phase space is rendered on the GPU.

C++ · GitHub

→ Check out Lael Costa's amazing browser-based billiards — honestly way better than mine!

COUGHVID

Reproducing published results on detecting COVID-19 infection from cough recordings, on a public dataset. University project at Heidelberg.

Python · Jupyter · Machine Learning · GitHub

Research

I'm a PhD student of James Farre, in the Geometry, Groups, and Dynamics research group (led by Anna Wienhard) and a member of the Mathematics Lab at the MPI MiS in Leipzig.

The main thread of my research is moduli spaces of dilation structures on spheres, and the dynamics of their straight-line foliations. These are other things I currently work and think about:

with Peter Doyle, Rich Schwartz, and Steve Trettel: proving that flat 8-vertex tori are universal, i.e. every modulus can be realized by an 8-vertex triangulation.
with Steve Trettel: classification of surfaces of revolution in homogeneous 3-manifolds.
with Charles Daly: symplectic tiling billiards on complete rational tori.
as part of a team in the lab: visualizing a class of aperiodic tilings of the hyperbolic plane, and developing an optimization library for (pseudo-)Riemannian geometry.
with Marit Bobb and Steve Trettel: machine learning to study the space of embedded flat 8-vertex tori in ℝ³.
computational rendering of polygonal representatives of dilation structures arising from meromorphic twisted 1-forms on low-complexity Riemann surfaces.

Writing

Posts

Degenerate Coaffine Representation Aug 2025
A visualization of the degenerate coaffine representation from the work of James Farre and Marit Bobb.
Ray marching flat surfaces Apr 2025
An interactive ray marching visualization for flat surfaces.
Reading Seminar: Translation Surfaces and Rational Billiards - The Veech Alternative Feb 2025
Seminar notes exploring Vorobets' approach to the Veech alternative — the dichotomy in geodesic flow behavior on translation surfaces: trajectories are either periodic or uniformly distributed.
Working with Python Virtual Environments for PyTorch Feb 2025
A practical guide to creating and using Python virtual environments for PyTorch development.
The n=4 Case Feb 2025
An illustration of half dilation structures on four punctured spheres, with interactive GeoGebra applets.