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LIMDA Joint Seminar: Arnau Padrol

  • LIMDA Joint Seminar: Arnau Padrol
  • 2016-11-02T12:00:00+01:00
  • 2016-11-02T23:59:59+01:00
  • Title: Colorful simplicial depth, Minkowski sums, and generalized Gale transforms. 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. Speaker: Arnau Padrol, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6).

Quan
02/11/2016 des de/d' 12:00"
On
Room 005, Modul C3, Campus Nord UPC
Més informació
https://combgraph.upc.edu/en/courses-and-seminars/limda-joint-seminar-announcements-2016-2017
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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.