You are cordially invited to the Topology Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Henry Adams (Colorado State University)<\/p>\n
“An introduction to Vietoris-Rips complexes”<\/p>\n
Abstract: I will give an introduction to Vietoris-Rips complexes and their uses in applied and computational topology. If a dataset is sampled from some unknown underlying space (say a manifold), then as more and more samples are drawn, the Vietoris-Rips persistent homology of the dataset converges to the Vietoris-Rips persistent homology of the manifold. But little is known about Vietoris-Rips complexes of manifolds. An exception is the case of the circle: I will describe how as the scale parameter increases, the Vietoris-Rips complexes of the circle obtain the homotopy types of the circle, the 3-sphere, the 5-sphere, …, until finally they are contractible. Much less is known about Vietoris-Rips complexes of spheres. I will also briefly explain how Vietoris-Rips complexes relate to generalizations of the Borsuk-Ulam theorem and to Gromov-Hausdorff distances between spheres.<\/p>\n
Date: 14 March, 2022
\nTime: 13:30 UTC+3<\/p>\n
This is an online seminar. To request the event link, please send a message to cihan.okay@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the Topology Seminar organized by the Department of Mathematics. Speaker: Henry Adams (Colorado State University) “An introduction to Vietoris-Rips complexes” Abstract: I will give an introduction to Vietoris-Rips complexes and their uses in applied and computational topology. If a dataset is sampled from some unknown [\u2026] <\/p>\n