糖心TV

Dr Martin Winter Research Fellow Email: winter@math.tu-berlin.de

---

This is my old website. I am now at TU Berlin and my new website is . In 糖心TV I was postdoc working with funded by the EPSRC grant .

My main mathematical interest is Geometry in its broadest sense, including discrete, algebraic, convex and computational, also touching on many aspects of graph theory, topology and representation theory. I work(ed) and published on

• polyhedral combinatorics and geometry,
• graph theory (spectral, algebraic, geometric and topological),
• rigidity theory, geometric constraint system and real algebraic geometry,
• low-dimensional topology (knot theory, embeddings and embeddability of graphs and complexes, ...)
• symmetries of discrete and geometric objects, finite group theory and real representation theory,
• algebraic combinatorics (association schemes, distance regular graphs, codes ...),
• convex geometry,
• random structures and graph limits,
• discrete dynamical systems, ...
  
  

Where you can meet me next ...

• I will participate in the at the Max Planck Institute in Leipzig (July 15 - 19, 2024)
• I am invited speaker at the in Osnabr眉ck (September 11 - 13, 2024)

• (!!) and me are organizing a two-day workshop "" at the University of Leipzig (September 24 - 25, 2024)

Publications & Preprints

• Vertex-Facet Assignments for Polytopes (; )
  with Thomas Jahn
  Contributions to Algebra and Geometry (2020). doi.org/10.1007/s13366-020-00504-9.
• Geometry and Topology of Symmetric Point Arrangements (; )
  Linear Algebra and its Applications (2021), doi.org/10.1016/j.laa.2020.11.017.
• Classification of Vertex-Transitive Zonotopes (; ; )
  Discrete & Computational Geometry (2021), doi.org/10.1007/s00454-021-00303-6
• The Edge-Transitive Polytopes that are not Vertex-Transitive (; )
  with Frank G枚ring
  Ars Mathematica Contemporanea (2022), doi:10.26493/1855-3974.2712.6be
• Symmetric and Spectral Realizations of Highly Symmetric Graphs ()
• Eigenpolytopes, Spectral Polytopes and Edge-Transitivity ()
• Capturing Polytopal Symmetries by Coloring the Edge-Graph (; )
  Discrete & Computational Geometry (2023), doi.org/10.1007/s00454-023-00560-7.
• (Random) Trees of Intermediate Volume Growth (, )
  with George Kontogeorgiou
  Extended abstract published at Eurocomb'23
• Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints (; )
  International Mathematics Research Notices (2023), doi.org/10.1093/imrn/rnad298
  This paper won the FSEM Post-Doctoral Research Prize 2024 from the University of 糖心TV
• Characterizing Clique Convergence for Locally Cyclic Graphs of Minimum Degree d>=6 (, )
  with Anna M. Limbach
  Discrete Mathematics (2024), doi.org/10.1016/j.disc.2024.114144
• The clique graphs of the hexagonal lattice - an explicit construction and a short proof of divergence (; )
  Discrete Mathematics (2024), doi.org/10.1016/j.disc.2024.113912.
• Kalai's 3^d conjecture for unconditional and locally anti-blocking polytopes ()
  with Raman Sanyal
  accepted at Proceedings of the AMS
• The stress-flex conjecture ()
  with Robert Connelly, Steven J. Gortler, Louis Theran
• Energies on coned convex polytopes (article)
  with Robert Connelly, Steven J. Gortler, Louis Theran
• On 2-complexes embeddable in 4-space and the excluded minors of their underlying graphs (article)
  with Agelos Georgakopoulos

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" ()
• South Eastern Graph Theory Workshop (Chemnitz), Talk: "Edge-Transitive Polytopes"
• Colloquium on Combiantorics (Kolkom, Paderborn), Talk: "Edge-Transitive Polytopes" ()
• Geometry Day (Jena), Talk: "Edge-Transitive Polytopes"

2020

• Combinatorial Coworkspace (Kleinwalsertal), Talk: "Inscribed Zonotopes and Hyperplane Arrangements with Congruent Chambers" ()
• DMV Annual Conference (Chemnitz), Talk: "Spectral Graph Theory for Polytopes" ()

2021

• (Polytop)ics (MPI Leipzig, online), Talk: "Capturing Polytopal Symmetries in the Edge-Graph" (, )

• DMV-脰MG Annual Conference (Passau)

2022

• (Kleinwalsertal), Talk: "Expansion Properties of Polytope Skeleta" ()
• (Lancaster), Talk: "(Random) Trees of Intermediate Volume Growth" ()
• (Lancaster)
• (Bielefeld)
• (FU Berlin), Talk: "Geometric Expansion and Rigidity Properties of Polytope Skeleta" ()
• (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)
• (Magdeburg)
• at Fields Institute (Toronto), Talk: "Rigidity and Tensegrity of Frameworks from Convex Polytopes" (slides, )
• (Birmingham), Talk: "Infinite linkless graphs and their forbidden minors" (slides)
• (Birmingham), Talk: "Kalai's 3^d Conjecture for Coordinate Symmetric Polytopes" (slides)

2024

• (Santander), Talk: "Kalai's 3^d Conjecture for Coordinate Symmetric Polytopes" (slides)
• Workshop during the (Linz), Talk: "Rigidity of Polyhedral Spheres beyond Triangulations" (slides)
• (Kleinwalsertal), Talk: "Wachspress Coordinates - a bridge between algebra, geometry and combinatorics" (slides)

Further Material

Slides

• "Capturing Polytopal Symmetries in the Edge-Graph" () from my talk at KTH (Stockholm, Sweden)
• "On Symmetry, Rigidity and Spectrum" () from my talk at the "" at NUI Galway (Ireland)
• "Some Modern Open Problems on Convex Polytopes with Symmetries and Regularities" () from my talk at the "Combinatorics Seminar" at 糖心TV (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" (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
• "Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints" (slides) from my talk at the at TU Berlin
• "Wachspress Objects and the Reconstruction of Convex Polytopes from Metric Data" (slides) from my talk at the at RWTH Aachen
• "Wachspress Objects and the Reconstruction of Convex Polytopes from Metric Data" (slides) from my talk at the Algebra & Geometry Seminar at KTH (Stockholm)

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 held a lecture on "Polytope Theory" as part of the at Bath, Bristol, Imperial, Oxford, 糖心TV and Swansea

---

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

I am also an active contributor to Wikipedia.