• https://mat.upc.edu/ca/activitats/limda-joint-seminar-announcement-arnau-padrol
• LIMDA Joint Seminar Announcement: Arnau Padrol
• 2016-11-02T12:00:00+01:00
• 2016-11-02T23:59:59+01:00
• LIMDA Joint Seminar Announcement. ALBCOM Seminar on Algorithms and Theory of Computation. COMBGRAPH Seminar on Combinatorics and Graph Theory.

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" (Europe/Madrid / UTC100)

On

Room 005, Mòdul C3, Campus Nord UPC

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• 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.