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
- !! Workshop announcement !! Georg Loho, Olivia Röhrig and I are organizing a 2-weeks hands-on workshop “Polyhedra in Lean” to take place August 24 – September 4, 2026 at FU Berlin. Registration is open and spots are limited.
- I am currently teaching “Geometry of Convex Polytopes” at MPI Leipzig.
- Our paper “Rigidity of polytopes with edge length and coplanarity constraints” (with Matthias Adrian-Himmelmann and Bernd Schulze) got published by IMRN (see arXiv for the free version)
What’s coming
- I will give a mini course on the “Geometry and Combinatorics of Rigidity” at FU Berlin during the Young Researchers Conference on Combinatorial Synergies (May 4 – 8, 2026).
- I am invited speaker at the Workshop Rigid Structures in Algebraic Combinatorics and Algebraic Statistics at the University of Edinburgh (May 18 – 22, 2026).
- I am giving an online talk in the “General Algebra” seminar of the Warsaw University of Technology (June 9, 2026).
- I will be at the Workshop Discrete Geometric Structures 2026 at TU Wien. I will give a short talk on “How to be non-afraid of non-convexity” (August 3 – 7, 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
I am an active user of the StackExchange network. Here are links to my mathematical profiles:
