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# "Colorful Simplicial Depth, Minkowski Sums, and Generalized Gale Transforms"

## Abstract for the Combinatorics Seminar 2017 November 14

In this paper (International Mathematics Research Notices, 2017) Adiprasito, Brinkmann, Padrol, Paták, Patáková, and Sanyal give a tight upper bound on the maximum number of colorful simplices that contain the origin, for generic point sets partitioned into color classes centered on the origin. Using a colorful variant of Gale duality, they show that this implies an upper bound on the the number of facets of a Minkowski sum of simplices that arise as the Minkowski sum of a facet of each simplex.