Dr Martin Winter
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Dr Martin WinterResearch Fellow |
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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). doi.org/10.1007/s13366-020-00504-9. - Geometry and Topology of Symmetric Point Arrangements (link; arXiv)
Linear Algebra and its Applications (2021), doi.org/10.1016/j.laa.2020.11.017. - Classification of Vertex-Transitive Zonotopes (open access; pdf; arXiv)
Discrete & Computational Geometry (2021), doi.org/10.1007/s00454-021-00303-6 - 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)
Accepted at Discrete & Computational Geometry (2022). - (Random) Trees of Intermediate Volume Growth (arXiv)
with G. Kontogeorgiou
Preprint, arXiv:2212.01883, December 2022.
accepted at Eurocomb'23 - Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints (arXiv)
Preprint, arXiv:2302.14194, February 2023. - Characterizing Clique Convergence for Locally Cyclic Graphs of Minimum Degree d>=6 (arXiv)
with Anna M. Limbach
Preprint, arXiv:2305.00503, May 2023
Conferences, Workshops, etc.
2018
- South Eastern Graph Theory Workshop (Chemnitz)
- FRICO (Chemnitz), Talk: "Spectral Methods for Symmetric Polytopes"
- South Eastern Graph Theory Workshop (Freiberg)
- Geomtry Day (Dresden)
2019
- 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"
2020
- Combinatorial Coworkspace (Kleinwalsertal), Talk: "Inscribed Zonotopes and Hyperplane Arrangements with Congruent Chambers" (slides)
- DMV Annual Conference (Chemnitz), Talk: "Spectral Graph Theory for Polytopes" (slides)
2021
- (Polytop)ics (MPI Leipzig, online), Talk: "Capturing Polytopal Symmetries in the Edge-Graph" (slides, video)
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DMV-ÖMG Annual Conference (Passau)
2022
- Combinatorial Coworkspace (Kleinwalsertal), Talk: "Expansion Properties of Polytope Skeleta" (slides)
- 29th British Combinatorial Conference (Lancaster), Talk: "(Random) Trees of Intermediate Volume Growth" (slides)
- LMS Research School on Knowledge Exchange in rigidity, flexibility and applications (Lancaster)
- Geometry meets Combinatorics (Bielefeld)
- DMV Annual Meeting (FU Berlin), Talk: "Geometric Expansion and Rigidity Properties of Polytope Skeleta" (slides)
- Symposium on Discrete Mathematics (Hamburg), Talk: "Using Izmestiev's Theorem - a tool in spectral polytope theory" (slides)
2023
- Graph Rigidity and Application (Lancaster), Talk: "Rigidity and Tensegrity of Frameworks from Polytopes" (slides)
Where you can meet me:
- I will be talking at the Seminar "Diskrete Mathematik/Geometrie & Diskrete Geometrie" at TU Berlin (May 31)
- I will participate and speak at the Workshop on Geometric Constraints at the Fields Institute (Toronto, Canada) (July 10 - 14)
- 24 Hours of Combinatorial Synergies in Magdeburg (June 28/29)
- 10th Heidelberg Laureate Forum (September 24 - 29)
Further Material
Slides
- "Capturing Polytopal Symmetries in the Edge-Graph" (extended slides) from my talk at KTH (Stockholm, Sweden)
- "On Symmetry, Rigidity and Spectrum" (slides) from my talk at the "School of Mathematical & Statistical Science" at NUI Galway (Ireland)
- "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" (slides) from my talk at the "Combinatorics Seminar" at Warwick (UK)
- "When Edges shrink then Polytopes become smaller - a proof in geometric polytope theory" (slides) from my talk at Pretoria University (South Africa)
- "(Random) Trees of Intermediate Volume Growth" (extended slides) from my talk in the Algorithms and Complexity seminar at Durham University
- "On 4-Flat Graphs and the Embeddability of 2-Complexes in Dimension Four" (slides) from my talk in the Discrete Geometry seminar at FU Berlin
PhD Thesis
My thesis "Spectral Realizations of Symmetric Graphs, Spectral Polytopes and Edge-Transitivity" and the slides of my defense talk.
Teaching
In the winter term 2022 I gave a lecture on "Polytope Theory" as part of the Taught Course Center (TCC, at Bath, Bristol, Imperial, Oxford, Warwick and Swansea)
I am an active user of the StackExchange network (username: M. Winter).
These are links to my mathematical profiles: