Dr Martin Winter

Dr Martin Winter

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

This is my old website. I am now Dirichlet Fellow at TU Berlin and my new website is here. In Warwick I was postdoc working with Agelos Georgakopoulos funded by the EPSRC grant "Graph Theory in Higher Dimensions".

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 Summer School "Algebraic Combinatorics" at the Max Planck Institute in Leipzig (July 15 - 19, 2024)
I am invited speaker at the Annual Conference of the SPP2458 "Combinatorial Synergies" in Osnabrück (September 11 - 13, 2024)
(!!) Rainer Sinn and me are organizing a two-day workshop "Wachspress Geometry" at the University of Leipzig (September 24 - 25, 2024)

Publications & Preprints

Vertex-Facet Assignments for Polytopes (open access; arXiv)
with Thomas 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 Frank Göring
Ars Mathematica Contemporanea (2022), doi:10.26493/1855-3974.2712.6be
Symmetric and Spectral Realizations of Highly Symmetric Graphs (arXiv)
Eigenpolytopes, Spectral Polytopes and Edge-Transitivity (arXiv)
Capturing Polytopal Symmetries by Coloring the Edge-Graph (open access; arXiv)
Discrete & Computational Geometry (2023), doi.org/10.1007/s00454-023-00560-7.
(Random) Trees of Intermediate Volume Growth (arXiv, extended abstract)
with George Kontogeorgiou
Extended abstract published at Eurocomb'23
Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints (open access; arXiv)
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 Warwick
Characterizing Clique Convergence for Locally Cyclic Graphs of Minimum Degree d>=6 (arXiv, open access)
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 (open access; arXiv)
Discrete Mathematics (2024), doi.org/10.1016/j.disc.2024.113912.
Kalai's 3^d conjecture for unconditional and locally anti-blocking polytopes (arXiv)
with Raman Sanyal
accepted at Proceedings of the AMS
The stress-flex conjecture (arXiv)
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" (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)
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)
24 Hours of Combinatorial Synergies (Magdeburg)
Workshop on Geometric Constraints at Fields Institute (Toronto), Talk: "Rigidity and Tensegrity of Frameworks from Convex Polytopes" (slides, video)
British Early Career Mathematicians' Colloquium (Birmingham), Talk: "Infinite linkless graphs and their forbidden minors" (slides)
Birmingham Warwick Joint Combinatorics Seminar (Birmingham), Talk: "Kalai's 3^d Conjecture for Coordinate Symmetric Polytopes" (slides)

2024

Workshop on Geometric and Algebraic Combinatorics (Santander), Talk: "Kalai's 3^d Conjecture for Coordinate Symmetric Polytopes" (slides)
Landscapes of Rigidity Workshop during the RICAM Special Semester on Rigidity and Flexibility (Linz), Talk: "Rigidity of Polyhedral Spheres beyond Triangulations" (slides)
Combinatorial Coworkspace (Kleinwalsertal), Talk: "Wachspress Coordinates - a bridge between algebra, geometry and combinatorics" (slides)

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" (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 Seminar "Diskrete Mathematik/Geometrie & Diskrete Geometrie" at TU Berlin
"Wachspress Objects and the Reconstruction of Convex Polytopes from Metric Data" (slides) from my talk at the Joint Algebra Seminar 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 Taught Course Center 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:

I am also an active contributor to Wikipedia.