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

I work at the intersection of combinatorics and algebra. My current research interests include freeness of hyperplane arrangements, matroid representations, asymptotics of matroids, supersolvable lattices and the generation of matroids. I enjoy using and developing computer algebra tools as part of my research.

Writing

In preparation

On the Comparison of Skew-linear and Multilinear Matroids (with Rudi Pendavingh and Geva Yashfe)
In preparation.

Preprints

The Universality of the Resonance Arrangement and its Betti Numbers
Submitted.
Representability of matroids by c-arrangements is undecidable (with Geva Yashfe)
Submitted.
Accepted as an extended abstract to FPSAC 2020.
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)
Submitted.
Locally heavy hyperplanes in multiarrangements (with Takuro Abe)
Submitted.

Published

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.

Workshop on Logarithmic Vector Fields and Freeness of Divisors and Arrangements at MFO, January 2021, Oberwohlfach, Germany
Workshop on Discrete Geometry at MFO, September 2020, Oberwohlfach, Germany
Arrangements at Home, August 2020, online
Formal Power Series and Algebraic Combinatorics (FPSAC), July 2020, online
Combinatorial Coworkspace — a session in algebraic and geometric combinatorics, March 2020, Kleinwalsertal, Austria
Algebraic Geometry - Varieties, Polyhedra, Computation, October 2019, FU Berlin
Hyperplane Arrangements and Reflection Groups, September 2019, Leibniz Universität Hannover
Canadian Discrete and Algorithmic Mathematics Conference, May 2019, Simon Fraser University, Vancouver
Arrangements at Western, May 2019, Western University, London Ontario
Spring School and Workshop on Polytopes, March 2019, Ruhr Universität Bochum
Combinatorial Geometries 2018, September 2018, CIRM
Summer School - New Perspectives in Hyperplane Arrangements, September 2018, Ruhr Universität Bochum
High-Dimensional Combinatorics, April 2018, IIAS Jerusalem
Einstein Workshop Discrete Geometry and Topology, March 2018, FU Berlin
Geometric and Topological Combinatorics, October 2017, MSRI
GAP Days 2017, 30th August - 1st September, Universität Siegen
Advances in Hyperplane Arrangements, August, Universität Bremen
Arrangements and beyond, June 2017, Scuola Normale Superiore, Pisa
Summer Conference on Hyperplane Arrangements, August 2016, Hokkaido University, Sapporo
Research stay to visit Takuro Abe, September 2015, Kyoto University

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.