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Combinatorial and algorithmic aspects of CAT(0) complexes

Date: Friday, November 15, 2019 10:00 - 11:00
Speaker: Hiroshi Hirai (University of Tokyo)
Location: Mondi Seminar Room 3, Central Building
Series: Mathematics and CS Seminar
Host: Vladimir Kolmogorov

Abstract:

A CAT(0) space is a geodesic metric space having globally non positive curvature.
In this talk, I will discuss combinatorial and algorithmic aspects of
CAT(0) spaces associated with
combinatorial objects (graphs, posets, etc), from applied mathematics points of view.
Topics include:
(1) The space of phylogenetic trees (Billera, Holmes, Vogtmann 2001), and Owen-Provan algorithm (Owen, Provan 2011) computing the geodesic between two phylogenetic trees, via parametric network flow.
(2) Orthoscheme complexes associated with posets (Brady-McCammond 2010), classes of lattices/semilattices having CAT(0) orthoscheme complexes, and their application to sub-modular optimization.
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