So teilt man Essen gerecht, auch wenn die Esser unterschiedliche Dinge mögen – oder im Hyperraum unterwegs sind.

YouTube video by Computational Geometry

We study the common intersection of arrangements of double-wedges. We consider arrangements where double-wedges may be either bowties (which do not contain a vertical line) or hourglasses (which conta...

The intermediate value theorem shows us how to find an even center on an irregular shape

What is this course about? This course studies modern graph algorithms through the lens of graph decomposition. Over the last two decades, expander decompositions and hierarchies have become some of ...

The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reconstructed using only...

New paper in cs.CG (Computational Geometry)

We consider colored variants of a class of geometric-combinatorial questions on $k$-gons and empty $k$-gons that have been started around 1935 by Erdős and Szekeres. In our setting we have $n$ points ...

New paper in cs.CG (Computational Geometry)

The famous Ham-Sandwich theorem states that any $d$ point sets in $\mathbb{R}^d$ can be simultaneously bisected by a single hyperplane. The $α$-Ham-Sandwich theorem gives a sufficient condition for th...

Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) fac...

We prove that there exist graphs which do not contain $K_t$ as an odd minor and whose chromatic number is at least $(\frac 32-o(1))t$. This disproves, in a strong form, the odd Hadwiger conjecture of ...