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Professur Algorithmische und Diskrete Mathematik
Martin Winter

Martin Winter, PhD

I am now a postdoc at the University of Warwick (UK), working with Agelos Georgakopoulos. I am funded by the EPSRC grant "Graph Theory in Higher Dimensions". This is my previous website, which will soon be replaced by one at Warwick.

Address: Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
Office: B2.28



Research Interests

  • polytope theory (combinatorial and geometric aspects; symmetry, rigidity, skeleta, ...),
  • graph theory (mostly spectral, algebraic, geometric and topological) grah theory,
  • embeddablity of graphs, simplicial complexes, CW-complexes,
  • symmetries of discrete and geometric objects (polytopes, graphs, compexes, ...),
  • algebraic combinatorics (association schemes, distance regular graphs, ...),
  • convex geometry,
  • group theory and representation theory,
  • low dimensional topology.

Publications & Preprints

  • T. Jahn and M. Winter.
    Vertex-Facet Assignments for Polytopes (open accessarXiv)
    Contributions to Algebra and Geometry (2020). doi.org/10.1007/s13366-020-00504-9.
  • M. Winter.
    Geometry and Topology of Symmetric Point Arrangements (linkarXiv)
    Linear Algebra and its Applications (2021), doi.org/10.1016/j.laa.2020.11.017.
  • M. Winter.
    Classification of Vertex-Transitive Zonotopes (open access; pdfarXiv)
    Discrete & Computational Geometry (2021), doi.org/10.1007/s00454-021-00303-6
  • F. Göring and M. Winter.
    The Edge-Transitive Polytopes that are not Vertex-Transitive (accepted manuscriptarXiv)
    Accepted at Ars Mathematica Contemporanea
  • M. Winter.
    Symmetric and Spectral Realizations of Highly Symmetric Graphs (arXiv)
    Preprint, arXiv:2009.01568, September 2020.
  • M. Winter.
    Eigenpolytopes, Spectral Polytopes and Edge-Transitivity (arXiv)
    Preprint, arXiv:2009.02179, September 2020.
  • M. Winter
    Capturing Polytopal Symmetries by Coloring the Edge-Graph (arXiv)
    Preprint, arXiv:2108.13483, September 2021.

Conferences, Workshops, etc.


  • South Eastern Graph Theory Workshop (Chemnitz)
  • FRICO (Chemnitz), Talk: "Spectral Methods for Symmetric Polytopes"
  • South Eastern Graph Theory Workshop (Freiberg)
  • Geomtry Day (Dresden)


  • Polytope Spring School (Bochum), Talk: "Spectral Methods for Symmetric Polytopes"
  • Summer School on Geometric & Algebraic Combinatorics (GAC, Paris)
  • Discrete Geometry Day^2 (Budapest), Talk: "Spectral Methods for Symmetric Polytopes" (slides)
  • South Eastern Graph Theory Workshop (Chemnitz), Talk: "Edge-Transitive Polytopes"
  • Colloquium on Combiantorics (Kolkom, Paderborn), Talk: "Edge-Transitive Polytopes" (slides)
  • Geometry Day (Jena), Talk: "Edge-Transitive Polytopes"


  • Combinatorial Coworkspace (Kleinwalsertal), Talk: "Inscribed Zonotopes and Hyperplane Arrangements with Congruent Chambers" (slides)
  • DMV Annual Conference (Chemnitz), Talk: "Spectral Graph Theory for Polytopes" (slides)
  • (Polytop)ics (MPI Leipzig, online), Talk: "Capturing Polytopal Symmetries in the Edge-Graph" (slides, video)
  • DMV-ÖMG Annual Conference (Passau)


  • Combinatorial Coworkspace (Kleinwalsertal), Talk: "Expansion Properties of Polytope Skeleta" (slides)

Upcoming event where you might meet me:

Further Material

  1. "Capturing Polytopal Symmetries in the Edge-Graph" (extended slides)
  2. "On Symmetry, Rigidity and Spectrum" (slides) from my talk at the "School of Mathematical & Statistical Science" at NUI Galway
  3. "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" (slides) from my talk at the "Combinatorics Seminar" at Warwick
PhD Thesis

My thesis "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity" and thes slides of my defense talk.


  • winter term 2018/19: Tutorial "Basics of Optimization"
  • winter term 2019/20: Tutorial "Graph Theory"
  • winter term 2020/21: Tutorial "Introduction to Discrete Mathematics"
  • Upcoming in October 2022: a graduate course in "Polytope Theory" (TCC lecture; Bath, Bristol, Imperial, Oxford and Warwick)

I am an active user of the StackExchange network (username: M. Winter).
These are links to my mathematical profiles:



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