Bisecting masses with hyperplane arrangements

Abstract: A hyperplane arrangement in $\mathbb{R}^ d$ divides space into two sets via a chessboard coloring. Given a set of measures, we can attempt to split each into two equal parts using the chessboard coloring of a hyperplane arrangement. Special cases of this problem include the classic ham sandwich theorem by Banach or the necklace splitting theorem by Hobby and Rice. We present a new common generalization of many mass partition results of this kind. Surprisingly, the proof methods are not topological, breaking a long tradition in the area. During this talk, we will describe the results that can be generalized this way and the reach of this new non-topological approach. Joint work with Alfredo Hubard.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology