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
- I am teaching “Geometry of Convex Polytopes” at MPI Leipzig. The course starts Friday, April 17 (the regular course is Wednesday, but in the first week it overlaps with the also very relevant Workshop on Metric Algebraic Geometry).
- 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)
- Kilian Rueß (UT Nürnberg) and John Maar (TU Berlin) have joined our formalization project for polyhedral geometry and combinatorics in Lean.
What’s coming
- I will visit Jan Kotrbatý at Charles University in Prague (April 14 – 15). I will speak in the Algebra Colloquium on April 14.
- Matthias Adrian-Himmelmann is visiting me at the MPI Leipzig and is speaking in the Nonlinear Algebra seminar (April 21).
- 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 will be at the Workshop Discrete Geometric Structures 2026 at TU Wien (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:
