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 relation between Mahler volume and flag number for convex polytopes”. We give a lower bound for the flag number of a convex polytope in terms of its Mahler volume. It shows that Kalai’s flag conjecture is implied by Mahler’s conjecture. Assuming the recently claimed resolution of Mahler’s conjecture by OpenAI, this proves Kalai’s flag conjecture.
- 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).
- It turned out that my 2023 paper contains a polytopal proof of Stoker’s conjecture! This was brough to my attention by Arseniy Akopyan. I wrote a short note about it.
What’s coming
- I will be at the “Ten Years Nonlinear Algebra” anniversery conference at MPI Leipzig (January 11 – 12, 2027).
- I will be speaking in the General Algebra Seminar at Warsaw University of Technologyy (January 14, 2027). I will be speaking on adjoints, canonical forms and Wachspress coordinates.
- I will speak in the “Geometry Lunch Seminar” at Pennsylvania State University (January 20, 2027). My talk will be on rigidity, polytopes and our resolution of Stoker’s conjecture.
- I will be visiting Klara Stokes at Umeå University in the week January 25 – 29, 2027. I will give a seminar talk on formalization, Lean and polyhedra.
- I will be at the SIAM Conference on Applied Algebraic Geometry at Osnabrück University (July 19 – 23, 2027). I will be speaking in the minisymposium “Theoremoids: Machine Mathematics and What We Do With It”. I am also co-organizing a minisymposium on “Rigidity Theory”.
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
Follow me on Mathstodon: @MWinter.
I am an active user of the StackExchange network. Here are links to my mathematical profiles:
