Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information
Date and Time: Tuesday, April 04, 2023, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Patrick Schnider
Tverberg's theorem is a fundamental theorem in discrete geometry which implies many other famous results such as Radons lemma and the Centerpoint theorem. It states that any r(d-1)+1 points in d-dimensional Euclidean space can be partitioned into r parts whose convex hulls have a common intersection. Motivated by an application in statistics, Rousseeuw and Hubert conjectured in 1999 that an analogue statement should be true when replacing "points" with "hyperplanes" and "convex hull" with "positive regression depth" (which will be defined in the talk). I will outline the motivation of the conjecture of Rousseeuw and Hubert by introducing combinatorial depth measures for hyperplane arrangements and show that the conjecture is true. This is joint work with Pablo Soberon.
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