Raphael Appenzeller

I am a mathematician working in Geometry and Geometric Group Theory. I am a postdoc at Heidelberg University in the working group of Petra Schwer. I used to be at ETH Zürich, where I completed my doctorate under the supervision of Marc Burger.

Contact me:

I like geometry. I like to create and look at models of mathematical objects. My research is about symmetric things with non-positive curvature. In my doctoral thesis I looked at connections between symmetric spaces and combinatorial objects called buildings.

Publications and preprints:

Preprint with José Pedro Quintanilha, Genus-zero links with prescribed knots as components, (2026). arXiv:2607.12729.
I wrote a blogpost about visualizing the main theorem.
Here are some pictuers of a genus zero surface whose boundary components are a left-handed trefoil, a right-handed trefoil, and a figure-eight knot, visualized using Inkscape, 3D-printing and crochet
with José Pedro Quintanilha, All knots are trivial: A "proof" by sleight of hand, Comptes Rendus - Série Mathématique 364 (2026), 529-544. doi:10.5802/crmath.843 🔓.
This paper served as the basis for a student seminar (for Lehramtstudierende) and as a consequence some of its content has actually been taught in highschools.
We also created some videos for this project.
Preprint with Xenia Flamm, Victor Jaeck. Morphisms of generalized affine buildings, (2026). arXiv:2601.04130.
Generalized affine buildings for semisimple algebraic groups over real closed fields, accepted for publication in Münster Journal of Mathematics (2026) 🔓 arXiv:2601.03226.
Preprint. Semisimple algebraic groups over real closed fields, (2026). arXiv:2601.07732.
with Kevin Klinge. Cops and robbers for hyperbolic and virtually free groups, Groups, Geometry and Dynamics (2026), published online first. doi:10.4171/GGD/959 🔓
with Auguste Hébert, Alexander Lytchak. Flat subsets of Euclidean buildings, accepted for publication in Münster Journal of Mathematics (2026) 🔓 arXiv:2512.11658.
Preprint with Schmitt, Bérczi, Dekoninck, Feusi, Gehrunger et al. IMProofBench: Benchmarking AI on Research-Level Mathematical Proof generation, (2025). arXiv:2509.26076.
You can join the IMProofBench-project too.
with Luca De Rosa, Xenia Flamm, Victor Jaeck. An incomplete real tree with complete segments, Innov. Incidence Geom. 21 (2024), 35–44. doi:10.2140/iig.2024.21.35i, arXiv:2212.09640.
(In)dependence of the axioms of Λ-trees, Analysis and Geometry in Metric Spaces 12(1) (2024). doi:10.1515/agms-2023-0106 🔓.
Parts of this project have been formalized in Lean3.

Here you can find my Bachelor Thesis on non-Archimedean hyperbolic planes and trees.

Together with Francesco Fournier-Facio, Simon Machado and Anand Rao Tadipatri we run the community blog Proofs and Prompts - Notes from the common room about AI and mathematics.

I like to 3D-print objects, some of which can be found on my thingiverse page. If you want to get a copy of the triangle shirt, you can buy one on spreadshirt.com.

Sometimes I like to create silly things. Here are some of them (very unpolished):

· arXiv · zbMATH · ORCID · thingiverse.com