Principal investigators

Prof. Dr. Lukas Kühne

Summary:

Project A7 is situated at the crossroads of algebra and combinatorics in the context of matroids. Matroids are combinatorial structures based on an abstraction of linear independence in vector spaces and are by now ubiquitous objects in mathematics admitting, for instance, a synthetic Hodge theory stemming from algebraic geometry. The first part of the project is concerned with matroids and arrangements of hyperplanes in light of Terao's freeness conjecture. The second part aims to investigate $q$-analogues of matroids and Coxeter matroids together with their relationships to modern coding theory.

Recent preprints:

24066 Emanuele Delucchi, Lukas Kühne, Leonie Mühlherr | |

Combinatorial invariants of finite metric spaces and the Wasserstein arrangement | |

Project: A7 |

24065 Sebastian Degen, Lukas Kühne | |

Most q-matroids are not representable | |

Project: A7 |

24052 Lukas Kühne, Dante Luber, Piotr Pokora | |

On the numerical Terao's conjecture and Ziegler pairs for line arrangements | |

Project: A7 |