Homepage of Lukas Kühne
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
Preprints
Published
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.
- 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
- Formal Power Series and Algebraic Combinatorics (FPSAC), July 2020, online
- 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