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.
- 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 access; arXiv)
Contributions to Algebra and Geometry (2020). doi.org/10.1007/s13366-020-00504-9.
- M. Winter.
Geometry and Topology of Symmetric Point Arrangements (link; arXiv)
Linear Algebra and its Applications (2021), doi.org/10.1016/j.laa.2020.11.017.
- M. Winter.
Classification of Vertex-Transitive Zonotopes (open access; pdf; arXiv)
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 manuscript; arXiv)
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:
- 29th British Combinatorial Conference (Lancaster, July 11 - 15)
- LMS Research School on Knowledge Exchange in rigidity, flexibility and applications (Lancaster, July 18 - 22)
- Geometry meets Combinatorics (Bielefeld, September 5 - 9)
- DMV Annual Meeting (Berlin, September 12 - 16)
Symposium on Discrete Mathematics (Hamburg, Sep 30 - Oct 1)
- "Capturing Polytopal Symmetries in the Edge-Graph" (extended slides)
- "On Symmetry, Rigidity and Spectrum" (slides) from my talk at the "School of Mathematical & Statistical Science" at NUI Galway
- "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" (slides) from my talk at the "Combinatorics Seminar" at Warwick
- 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: