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.
- 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.
02/11/2016 des de 12:00 (Europe/Madrid / UTC100)
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).
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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.
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