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Dr Martin Winter

  A picture of me

Dr Martin Winter

Research Fellow
Office: B2.28
Phone: +44 (0)24 765 23972

I am a postdoc working with Agelos Georgakopoulos. I am funded by the EPSRC grant "Graph Theory in Higher Dimensions".

Research Interests
  • polytope theory (combinatorial and geometric aspects; symmetry, rigidity, skeleta, ...),
  • graph theory (spectral, algebraic, geometric and topological),
  • embeddability 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
  • Vertex-Facet Assignments for Polytopes (open access; arXiv)
    with T. Jahn
    Contributions to Algebra and Geometry (2020).
  • Geometry and Topology of Symmetric Point Arrangements (link; arXiv)
    Linear Algebra and its Applications (2021),
  • Classification of Vertex-Transitive Zonotopes (open access; pdf; arXiv)
    Discrete & Computational Geometry (2021),
  • The Edge-Transitive Polytopes that are not Vertex-Transitive (link; arXiv)
    with F. Göring
    Ars Mathematica Contemporanea (2022), doi:10.26493/1855-3974.2712.6be
  • Symmetric and Spectral Realizations of Highly Symmetric Graphs (arXiv)
    Preprint, arXiv:2009.01568, September 2020.
  • Eigenpolytopes, Spectral Polytopes and Edge-Transitivity (arXiv)
    Preprint, arXiv:2009.02179, September 2020.
  • Capturing Polytopal Symmetries by Coloring the Edge-Graph (arXiv)
    Preprint, arXiv:2108.13483, September 2021.
  • (Random) Trees of Intermediate Volume Growth (arXiv)
    with G. Kontogeorgiou
    Preprint, arXiv:2212.01883, December 2022.
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)


Further Material


  1. "Capturing Polytopal Symmetries in the Edge-Graph" (extended slides) from my talk at KTH (Stockholm, Sweden)
  2. "On Symmetry, Rigidity and Spectrum" (slides) from my talk at the "School of Mathematical & Statistical Science" at NUI Galway (Ireland)
  3. "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" (slides) from my talk at the "Combinatorics Seminar" at Warwick (UK)
  4. "When Edges shrink then Polytopes become smaller - a proof in geometric polytope theory" (slides) from my talk at Pretoria University (South Africa)

PhD Thesis

My thesis "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity" and the 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"
  • winter term 2022: lecture "Polytope Theory" (TCC course; 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: