Building on the work of Pach, Rubin, and Tardos, we prove that every set of $n\ge2$ points in the real plane with no three collinear contains at least $cn$ pairwise crossing segments with distinct end...

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 ...