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
- !! Registration Open !! Together with Timo de Wolff and Matthias Himmelmann, we are organizing the workshop Positivity, Convexity and Computation in Rigidity Theory to take place February 26 – 27, 2026 at TU Braunschweig.
- New preprint “The canonical form, scissors congruence and adjoint degrees of polytopes” with Tom Baumbach, Ansgar Freyer and Julian Weigert [arXiv]
What’s coming
- I will be at the workshop Developments in Algorithmic, Discrete and Tropical Geometry at the Zuse Institute Berlin (February 2 – 4, 2026).
- I am speaking in the Obserseminar Kombinatorik at the Ruhr-University Bochum (February 10).
- I co-organize the Workshop Positivity, Convexity and Computation in Rigidity Theory at TU Braunschweig (February 26 – 27, 2026). Before that I will speak in the Applied Algebra Seminar (February 25).
- I will be at the Workshop Combinatorics, Algorithms, and Geometry at the University of Kassel (March 2 – 6, 2026).
- 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 at FU Berlin during the Young Researchers Spring School (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
- 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:
