Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler
conjecture for symmetric convex bodies. Our contributions include, in particular, simple self …

In this paper we study envy‐free division problems. The classical approach to such
problems, used by David Gale, reduces to considering continuous maps of a simplex to itself …

Discrete geometry on colored point sets in the plane has a long history, but this research
area has been extensively developed in the last 2 decades. In 2003, a short survey entitled …

This article has two goals. First, we hope to give an accessible introduction to persistent
equivariant cohomology. Given a topological group $ G $ acting on a filtered space …

A problem is solved or some other goal achieved by “topological methods” if in our
arguments we appeal to the “form,” the “shape,” the “global” rather than “local” structure of …

We prove that, for any positive integer m, a segment may be partitioned into m possibly
degenerate or empty segments with equal values of a continuous function f evaluated on …

We study nested partitions of R d obtained by successive cuts using hyperplanes with fixed
directions. We establish the number of measures that can be split evenly simultaneously by …

We prove a common generalization of the Ham Sandwich theorem and Alon's Necklace
Splitting theorem. Our main results show the existence of fair distributions of m measures in …

We use recent extensions of the Borsuk–Ulam theorem for Stiefel manifolds to generalize
the ham sandwich theorem to mass assignments. A k-dimensional mass assignment …