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LIMDA Joint Seminar Announcement: Arnau Padrol

LIMDA Joint Seminar Announcement. ALBCOM Seminar on Algorithms and Theory of Computation. COMBGRAPH Seminar on Combinatorics and Graph Theory.

Quan
02/11/2016 des de/d' 12:00"
On
Room 005, Mòdul C3, Campus Nord UPC
iCal
  • Speaker: Arnau Padrol, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6).

  • Title: Colorful simplicial depth, Minkowski sums, and generalized Gale transforms.

Abstract

The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained in their convex hull. We use methods from combinatorial topology to prove a tight upper bound on the colorful simplicial depth. This implies a conjecture of Deza et al. (2006). Furthermore, we introduce colorful Gale transforms as a bridge between colorful configurations and Minkowski sums. Our colorful upper bound then yields a tight upper bound on the number of totally mixed facets of certain Minkowski sums of simplices. This resolves a conjecture of Burton (2003) in the theory of normal surfaces.

This is joint work with Adiprasito, Brinkmann, Paták, Patáková and Sanyal.