Lukas Kühne

About

Contact

Research

Writing

Preprints

1. When alcoved polytopes add
   with Nick Early and Leonid Monin.
   
2. Arrangements and Likelihood
   with Thomas Kahle, Leonie Mühlherr, Bernd Sturmfels and Max Wiesmann.
   
3. Combinatorial invariants of finite metric spaces and the Wasserstein arrangement
   with Emanuele Delucchi and Leonie Mühlherr.
   
4. Most q-matroids are not representable
   with Sebastian Degen.
   
5. On the numerical Terao's conjecture and Ziegler pairs for line arrangements
   with Dante Luber and Piotr Pokora.
   
6. Regular polygons, line operators, and elliptic modular surfaces as realization spaces of matroids
   with Xavier Roulleau.
   
7. On entropic and almost multilinear representability of matroids
   with Geva Yashfe.
   

Published or accepted for publication

1. Dynamical systems on some elliptic modular surfaces via operators on line arrangements
   with Xavier Roulleau.
   To appear in Nagoya Mathematical Journal. (arXiv)
2. Projective dimension of weakly chordal graphic arrangements
   with Takuro Abe, Paul Mücksch, and Leonie Mühlherr.
   To appear in Algebraic Combinatorics.
3. Matroids in OSCAR
   with Daniel Corey and Benjamin Schröter.
   To appear in as a chapter in the book The Computer Algebra System OSCAR.
4. Line arrangements with many triple points
   with Tomasz Szemberg and Halszka Tutaj-Gasińska.
   Rendiconti del Circolo Matematico di Palermo Series 2 (2024).(arXiv)
5. Faces of Cosmological Polytopes
   with Leonid Monin.
   To appear in Annales de l’Institut Henri Poincaré D. (arXiv)
6. On arrangements of hyperplanes from connected subgraphs
   with Michael Cuntz.
   To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. (arXiv)
7. Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries
   with Taylor Brysiewicz and Holger Eble.
   Discrete & Computational Geometry. (arXiv)
8. Computing the nonfree locus of the moduli space of arrangements and Terao's freeness conjecture
   with Mohamed Barakat.
   Mathematics of Computation, 92 (2023), pp. 1431-1452. (arXiv)
   An extended abstract appeared in the Oberwolfach workshop report 5/2021 and in the Computeralgebra Rundbrief Ausgabe 68.
9. On the geometry of flag Hilbert-Poincaré series for matroids
   with Joshua Maglione.
   Algebraic Combinatorics, 6(3), (2023), pp. 623-638. (arXiv)
   An extended abstract appeared in the proceedings of the conference Formal Power Series and Algebraic Combinatorics (FPSAC 2022).
   
10. Likelihood Degenerations
    with Daniele Agostini, Taylor Brysiewicz, Claudia Fevola, Bernd Sturmfels, and Simon Telen.
    Advances in Mathematics, 414 (2023), Paper No. 108863. (arXiv)
    
11. Von Staudt Constructions for Skew-Linear and Multilinear Matroids
    with Rudi Pendavingh and Geva Yashfe.
    Combinatorial Theory, 3(1) (2023), Paper No. 16. (arXiv)
    
12. The Universality of the Resonance Arrangement and its Betti Numbers.
    Combinatorica (2023). (arXiv)
    An extended abstract appeared in the proceedings of the conference Formal Power Series and Algebraic Combinatorics (FPSAC 2021).
13. Representability of Matroids by c-Arrangements is Undecidable
    with Geva Yashfe.
    Israel Journal of Mathematics, 252, (2022), pp. 95–147. (arXiv)
    An extended abstract appeared in the proceedings of the conference Formal Power Series and Algebraic Combinatorics (FPSAC 2020).
    
14. Locally heavy hyperplanes in multiarrangements
    with Takuro Abe.
    Journal of Pure and Applied Algebra, 226(1), (2022) Paper No. 106791. (arXiv)
15. On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
    with Mohamed Barakat, Reimer Behrends, Christopher Jefferson, and Martin Leuner.
    SIAM Journal of Discrete Mathematics, 35(2), (2021) pp. 1201-1223. (arXiv)
16. Heavy hyperplanes in multiarrangements and their freeness
    with Takuro Abe.
    Journal of Algebraic Combinatorics, 48, (2018), pp. 581–606. (arXiv)

Software

Teaching

PhD students

• Fenja Mehlan, 2024 - present, funded by DFG SPP 2458
• Sebastian Degen, 2023 - present, funded by DFG SFB-TRR 358
• Leonie Mühlherr, 2022 - present

Selected grants