## 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, November 27, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Patrick Schnider

## Ham Sandwich Cuts in Subspaces

The famous Ham Sandwich Theorem states that given any d mass distributions in d-dimensional space, we can find a hyperplane that simultaneously bisects all of them. for n> d, a d-dimensional space can be seen as one of many linear subspaces of a larger n-dimensional space. Suppose now that you are given a continuous assignment of mass distributions to every linear d-dimensional subspace of this n-dimensional space. Is there a subspace where you can simultaneously bisect more than d mass distributions? The answer is yes, there is always a subspace in which you can simultaneously bisect n mass distributions. Further, at the expense of some mass distributions, you can further restrict the subspace to contain some fixed vectors. Finally, some of the results extend to the more general notion of center transversals. In this talk, we will look at some concepts used in the proof of this result.

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