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 working on the formalization of polyhedral geometry in Lean (see the work in progress on GitHub).

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 just returning from a productive week at the Workshop Combinatorics, Algorithms, and Geometry at the University of Kassel. I met many new great people and learned a lot about quiver mutations and transportation polytopes.
• Our paper “Rigidity of polytopes with edge length and coplanarity constraints” (with Matthias Himmelmann and Bernd Schulze) got accepted at IMRN!
• Kilian Rueß (UT Nürnberg) and John Maar (TU Berlin) have now joined our project formalizing polyhedral geometry and combinatorics in Lean
• We had a sucessful workshop Workshop Positivity, Convexity and Computation in Rigidity Theory at TU Braunschweig (February 26 – 27), co-organized with Matthias Himmelmann and Timo de Wolff. You can find the group photo here.

What’s coming

• I will be at the Workshop on Polyhedral Geometry for Neural Networks at the University of Technology Nuremberg (March 16 – 20, 2026).
• In the summer term 2026 I will give a lecture “Geometry of Convex Polytopes” at the MPI Leipzig.
• 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 will be 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:

• MathOverflow
• Math.StackExchange