Martin Winter, PhD
martin.winter@mis.mpg.de
I am a mathematician. I am member of the Nonlinear Algebra group at the Max-Planck-Institute for Mathematics in the Sciences in Leipzig and principal investigator in the priority program Combinatorial Synergies.
My research is in discrete geometry, real algebraic geometry, geometric rigidity, semi-definite optimization, spectral graph theory, algebraic combinatorics and low-dimensional topology. Most recently I am studying the Wachspress Geometry of convex polytopes. I am also leading a Lean formalization project about polyhedral geometry and combinatorics.
Until 2025 I was Dirichlet fellow at TU Berlin. Before I was postdoc at the University of Warwick (UK). I got my PhD from TU Chemnitz (Germany) in 2021.
What’s new
- New preprint. “A short polyhedral proof of the infinitesimal Stoker conjecture”. I also wrote a second version using the Alexandrov matrix (not entirely cleaned up yet).
- Arseniy Akopyan with ChatGPT noticed that my 2023 paper contained a polytopal proof of Stoker’s conjecture! I wrote a short note about it. Karim Adiprasito also mentions this on his blog. :)
- We just finished the workshop “Polyhedra in Lean” that I co-organized with Georg Loho and Olivia Röhrig at FU Berlin. We had a well-attended two weeks of hands-on coding for the formalization of polyhedral mathematics. It was a huge sucess – we now have many new contributors to mathlib and our polyhedral repository. Also check out the workshop website for the group photos!
- New preprint. “Shallower ReLU Network Representations via Exact Linear Algebra” (with Kilian Rueß, Gennadiy Averkov, Florestan Brunck, Moritz Grillo, Christoph Hertrich, Georg Loho, Jack Stade, Moritz Stargalla and Matthew Sun). We prove that a ReLU network can represent the maximum of 10 real numbers with onyl two hidden layers.
What’s coming
- I will participate in the Conference “Positive Geometry Beyond Physics” at MPI Leipzig (October 21 – 23, 2026).
Selected publications
- The canonical form, scissors congruence and adjoint degrees of polytopes [arXiv]
with Tom Baumbach, Ansgar Freyer and Julian Weigert - Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints [arXiv, journal]
This paper won the FSEM Post-Doctoral Research Prize 2024 from the University of Warwick - Kalai’s \(3^d\) conjecture for unconditional and locally anti-blocking polytopes [arXiv, journal]
with Raman Sanyal - “Rigidity of polytopes with edge length and coplanarity constraints” [arXiv, journal]
with Matthias Adrian-Himmelmann and Bernd Schulze
I am an active user of the StackExchange network. Here are links to my mathematical profiles:
