Homepage of Lukas Kühne

I am a postdoctoral researcher in the Nonlinear Algebra group of Bernd Sturmfels at the Max Planck Institute of Mathematics in the Sciences in Leipzig.
Previously, I was a PhD student in mathematics at Hebrew Universiy of Jerusalem where my advisor was Karim Adiprasito.
Here is my CV.

Contact Information

lukas DOT kuhne AT mis DOT mpg DOT de
Office F3 06
Max Planck Institute for Mathematics in the Sciences
Inselstraße 22
04103 Leipzig, Germany

Research Interests

My research lies at the crossroads of algebra, combinatorics, algebraic geometry, and algorithms. My current interests include hyperplane arrangements, matroids and tropical geometry. I enjoy using and developing computer algebra tools as part of my research.

Writing

In Preparation

Computing the nonfree locus of the moduli space of arrangements and Terao's freeness conjecture
(with Mohamed Barakat)
An extended abstract appeared in the Oberwolfach Workshop report 05/2021.

Preprints

Likelihood Degenerations
(with Daniele Agostini, Taylor Brysiewicz, Claudia Fevola, Bernd Sturmfels, and Simon Telen)
Enumerating chambers of hyperplane arrangements with symmetry
(with Taylor Brysiewicz and Holger Eble)
Von Staudt Constructions for Skew-Linear and Multilinear Matroids
(with Rudi Pendavingh and Geva Yashfe)
The Universality of the Resonance Arrangement and its Betti Numbers
An extended abstract appeared in the proceedings of the conference Formal Power Series and Algebraic Combinatorics (FPSAC 2021).

Published

Representability of matroids by c-arrangements is undecidable (with Geva Yashfe)
An extended abstract appeared in the proceedings of the conference Formal Power Series and Algebraic Combinatorics (FPSAC 2020).
Accepted for publication in Israel Journal of Mathematics.
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 J. Discrete Math., 35(2), (2021) 1201-1223. (arXiv)
Locally heavy hyperplanes in multiarrangements (with Takuro Abe)
Journal of Pure and Applied Algebra 226 (2022). (arXiv)
Heavy hyperplanes in multiarrangements and their freeness (with Takuro Abe)
Journal of Algebraic Combinatorics 48 (2018), pp. 581–606. (arXiv)

Software

In joint work with Mohamed Barakat, I wrote the GAP package MatroidGeneration to create an ArangoDB database of all rank 3 matroids up to size 14 whose characteristic polynomial factors over the integer.
These matroids are among others relevant in the study of free or supersolvable hyperplane arrangements. Feel free to try it and contact us for questions, suggestions or feedback.

Previously, I worked at the Research Insitute for Discrete Mathematics in Bonn to develop and apply tools from combinatorial optimization in a a chip design project in cooperation with IBM.

Travel

A list of conferences where I have been/expect to be.

SIAM Conference on Applied Algebraic Geometry at Texas A&M University, August 2021, online attendance
Semester Program on Combinatorial Algebraic Geometry at ICERM, February - May 2021, Brown University, USA, online attendance
Workshop on Logarithmic Vector Fields and Freeness of Divisors and Arrangements at MFO, January 2021, Oberwohlfach, Germany, online attendance
Workshop on Discrete Geometry at MFO, September 2020, Oberwohlfach, Germany
Arrangements at Home, August 2020, online attendance
Formal Power Series and Algebraic Combinatorics (FPSAC), July 2020, online attendance
Combinatorial Coworkspace — a session in algebraic and geometric combinatorics, March 2020, Kleinwalsertal, Austria, Germany
Algebraic Geometry - Varieties, Polyhedra, Computation, October 2019, FU Berlin, Germany
Hyperplane Arrangements and Reflection Groups, September 2019, Leibniz Universität Hannover, Germany
Canadian Discrete and Algorithmic Mathematics Conference, May 2019, Simon Fraser University, Vancouver, Canada
Arrangements at Western, May 2019, Western University, London (ON), Canada
Spring School and Workshop on Polytopes, March 2019, Ruhr Universität Bochum, Germany
Combinatorial Geometries 2018 at CIRM, September 2018, Luminy, France
Summer School - New Perspectives in Hyperplane Arrangements, September 2018, Ruhr Universität Bochum, Germany
High-Dimensional Combinatorics, April 2018, IIAS Jerusalem, Israel
Einstein Workshop Discrete Geometry and Topology, March 2018, FU Berlin, Germany
Geometric and Topological Combinatorics, October 2017, MSRI, USA
GAP Days 2017, August 2017, Universität Siegen, Germany
Advances in Hyperplane Arrangements, August, Universität Bremen, Germany
Arrangements and beyond, June 2017, Scuola Normale Superiore, Pisa, Italy
Summer Conference on Hyperplane Arrangements, August 2016, Hokkaido University, Sapporo, Japan
Research stay to visit Takuro Abe, September 2015, Kyoto University, Japan

Teaching

In 2014 and 2015, I held tutorials for the lectures Linear Algebra I and Analysis II in Bonn. From 2012 to 2014, I gave tutorials in Kaiserslautern for the lectures Fundamentals of Mathematics I and II, Algebraic Structures and Elementary Number Theory.
I gave summer courses for gifted high school students at the German Pupils Academy (Deutsche Schülerakademie) on linear optimization (2016 and 2018) and topological data analysis (2019).

Other

Miscellaneous programs I participated in: International Summer Science Institute, Deutsche Schülerakademie, Bundeswettbewerb Mathematik and Früheinstieg ins Mathematikstudium.

My PhD studies are funded by the Minerva Stiftung and the Studienstiftung des deutschen Volkes.