Graduate Geometry, Topology and Dynamics Seminar
Jānis Lazovskis
UIC
Geometrically motivated partial orders on simplicial complexes
Abstract: A simplicial complex is a pair $(V,S)$, where $V$ is a (finite) set and $S$ is a subset of the power set $\mathcal P(V)$ closed under taking appropriate subsets ("faces"). The natural partial order from this definition is inclusion, which also makes some geometric sense. I will introduce two other partial orders, based on the Vietoris-Rips and Čech constructions of a simplicial complex from a vertex set and a radius. These orders correspond with the interpretation of a "path" in the universal space over the product of the Ran space (space of all finite subsets of some other space) and the non-negative real numbers.
Thursday April 26, 2018 at 4:00 PM in SEO 636