[Com-top_seminars] Course: Gromov-Hausdorff Distance in Computational Topology

[MANUEL SORIANO TRIGUEROS]

Hello everyone,

We are pleased to announce that Nicolò Zava will be delivering a 5-hour short course on the Gromov-Hausdorff distance and its role in stability theorems in computational topology.

The course will run from May 11th to 14th. The sessions are designed to be progressive: starting with an introduction to metric geometry accessible to all, and concluding with advanced applications to persistent homology.

Nicolò Zava<https://sites.google.com/view/nicolozava/home> is a postdoc at the Institute of Science and Technology Austria (ISTA) in Herbert Edelsbrunner's research group. He is interested in using metric geometry and dimension theory for comparing datasets and discussing their complexity.

Title: Gromov-Hausdorff distance and stability results in computational topology
Where and when: all classes will be held at the White Building (E.T.S. Informática), Reina Mercedes.
    - Monday 11th May | 12:30-14:10 | Aula A1.11
    - Tuesday 12th May | 10:00-11:40 | Aula A2.13
    - Thursday 14th May |10:00-11:40 | Aula A2.13
Language: English
Link:  https://www.imus.us.es/#actividad/3458

Planning

Lecture 1:

  *   Metric spaces and examples
  *   Desired properties for shape comparison
  *   History and definition: Hausdorff, Hausdorff under isometry, and Gromov-Hausdorff distance
  *   Characterisations using either correspondences or pairs of maps Basic properties

Lecture 2:

  *   Existence of distortion-minimising correspondences
  *   The Gromov-Hausdorff distance is a metric
  *   Mention of some of its metric, topological, dimensional, and embeddability properties
  *   Stable invariants: examples and a few computations
  *   Stability of Vietoris-Rips persistence diagrams

Lecture 3:

  *   Recall of stability of Vietoris-Rips persistence diagrams
  *   Extension of Gromov-Hausdorff motivated by stability results
  *   There are two "different sets": Gromov-Hausdorff between metric pairs and stability of Dowker and ambient Čech persistence diagrams
  *   Chromatic topological data analysis: chromatic metric spaces (and pairs) and six-pack
  *   C-constrained Gromov-Hausdorff distance: definition via maps and basic properties
  *   Stability of the six-pack

Best,

Manuel Soriano Trigueros
Prof. Ayudante Doctor / Assistant Professor

Dpto de Ciencias de la Computación e Inteligencia Artificial
Universidad de Sevilla
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