Résumé : Combinatorial depth measures are a way to generalize the concept of medians to higher dimensions, formalizing our intuition that some query points lie „deeper“ within a set of data points than others. Several such measures have been introduced in the last century, such as Tukey depth or Simplicial depth. Many fundamental problems in discrete geometry, such as the centerpoint theorem or Tverberg’s theorem, can be phrased naturally in terms of depth measures. In my talk, I consider families of combinatorial depth measures defined by natural sets of axioms and show that they cannot differ too much.

 [Slides.pdf] [article] [vidéo]

Dernière modification : Monday 18 March 2024

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr