## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, February 26, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Patrick Schnider

## Center transversals in subspaces

The center transversal theorem is a result which generalizes both the centerpoint theorem and the Ham-Sandwich theorem, two famous theorems from discrete geometry. The statement of the center transversal theorem is as follows: Given any k mass distributions in d-dimensional space, there exists a (k-1)-dimensional affine subspace g, called a (k-1)-center transversal, such that any halfspace containing g contains at least a (1/(d-k+2))-fraction of each mass. Setting k=d, we get the statement of the Ham-Sandwich theorem, while setting k=1 gives the centerpoint theorem. Assume now that you are given a continuous assignment of t mass distributions to every linear d-dimensional subspace of an n-dimensional space. Is there a subspace where you can find a center transversal for more than d masses? The answer is yes, there is always a subspace where you can find a (k-1)-center transversal for t=k+n-d masses. In this talk, which can be seen as a continuation of my last talk "Ham Sandwich Cuts in Subspaces", we will look at some concepts used in the proof of this result.

Information for students and suggested topics for student talks