Curvature Sets Over Persistence Diagrams

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Mario Gomez Flores
November 9, 2021
4:00PM - 5:00PM
Location
Zoom

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Add to Calendar 2021-11-09 16:00:00 2021-11-09 17:00:00 Curvature Sets Over Persistence Diagrams Title:  Curvature Sets Over Persistence Diagrams Speaker:  Mario Gómez Flores (Ohio State University) Abstract:  We study an invariant of compact metric spaces inspired by the Curvature Sets defined by Gromov. The (n,k)-Persistence Set of X is the collection of k-dimensional VR persistence diagrams of any subset of X with n or less points. This research seeks to provide a cheaper persistence-like invariant for metric spaces, as the computation of the VR complex becomes prohibitive once the input reaches a certain size. I'll focus on the case n=2k+2, where we can find a geometric formula to calculate the VR persistence diagram of a space with n points. We explore the application of this formula to the characterization of persistence sets of several spaces, including circles, higher dimensional spheres, and surfaces with constant curvature. We also show that persistence sets can detect the homotopy type of a certain family of graphs. URL associated with Seminar https://tgda.osu.edu/activities/tdga-seminar/ Zoom Department of Mathematics math@osu.edu America/New_York public
Description

Title:  Curvature Sets Over Persistence Diagrams

Speaker:  Mario Gómez Flores (Ohio State University)

Abstract:  We study an invariant of compact metric spaces inspired by the Curvature Sets defined by Gromov. The (n,k)-Persistence Set of X is the collection of k-dimensional VR persistence diagrams of any subset of X with n or less points. This research seeks to provide a cheaper persistence-like invariant for metric spaces, as the computation of the VR complex becomes prohibitive once the input reaches a certain size. I'll focus on the case n=2k+2, where we can find a geometric formula to calculate the VR persistence diagram of a space with n points. We explore the application of this formula to the characterization of persistence sets of several spaces, including circles, higher dimensional spheres, and surfaces with constant curvature. We also show that persistence sets can detect the homotopy type of a certain family of graphs.

URL associated with Seminar
https://tgda.osu.edu/activities/tdga-seminar/

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