Events & Calendar

Homotopical Perspectives on Topological Data Analysis
Jun 02, 2022 to Jun 02, 2022

Location : ONLINE TBA

This is an event organized jointly with the Center of Topology and Quantum Computing in Abu Dhabi, UAE.
 
Topological Data Analysis is a strongly emerging branch of Algebraic Topology that is finding important applications in many fields of science. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data by combining algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape".
 
Thursday June 2
 
    3-4pm : Ling Zhou ( Ohio State University, USA)
    4-5pm : Wojciech Chacholski  (KTH, Sweden)
    little break
    5h30-6h30 :  Grégory Ginot  (Université Paris 13 - France

    6h30-7h30 : Rick Jardine  (Western University, Canada)

Organizing Commitee:
Center of Topology and Quantum Computing, MIMS

Scientific Commitee:
Hisham Sati, Sadok Kallel

Sponsors:
CTQ, MIMS

Rick Jardine

TBA

Wojciech Chacholski

TBA

Grégory Ginot

Homotopical and sheaf theoretic point of view on multi-parameter persistence.

Abstract: In this talk we will highlight the study of level set persistence through the prism of sheaf theory and a special type of 2-parameter persistence : Mayer-Vietoris systems and a pseudo-sometry between those. This is based on joint work with Berkouk and Oudot.

Ling Zhou

Persistent homotopy groups of metric spaces

Abstract: By capturing both geometric and topological features of datasets, persistent homology has shown its promise in applications. Motivated by the fact that homotopy in general contains more information than homology, we study notions of persistent homotopy groups of compact metric spaces, together with their stability properties in the Gromov-Hausdorff sense. Under fairly mild assumptions on the spaces, we proved that the classical fundamental group has an underlying tree-like structure (i.e. a dendrogram) and an associated ultrametric. We then exhibit pairs of filtrations that are confounded by persistent homology but are distinguished by their persistent homotopy groups. We finally describe the notion of persistent rational homotopy groups, which is easier to handle but still contains extra information compared to persistent homology.

Thursday June 2 (online):
 
    3-4pm : Ling Zhou ( Ohio State University, USA)
    4-5pm : Wojciech Chacholski  (KTH, Sweden)
    little break
    5h30-6h30 :  Grégory Ginot  (Université Paris 13 - France

    6h30-7h30 : Rick Jardine  (Western University, Canada)

List of participants to this conference
Jun 02, 2022 to Jun 02, 2022

No participants
Contact
secretary@mims-institut.org