Topological Persistence
Theory and Applications
Abstract
The course is focused on one of the tools of computational topology, currently among the most used in shape and data analysis: persistent homology. Basic concepts of algebraic topology will be introduced, necessary to be able to retrace the classical results of the theory of persistent homology up to the recent developments of Topological machine learning and the numerous applications, which range from signal and image processing to the classification of graphs and networks, from analysis of three-dimensional shapes up to the monitoring of machine learning processes.
News
[26/01/2024] The Minicourse on "Dynamical Systems, Algebraic Topology, and Climate" by Michael Ghil from ENS Paris, UCLA, and Imperial College London and Denisse Sciamarella from IFAECI (CNRS) and the University of Buenos Aires will be held on Tues. 13 Feb. 14:00-16:00, Thurs. 15 Feb. 14:00-16:00, and Tues. 20 Feb 14:00-16:00. Platform: Online via Zoom/ Using the usual link: https://us02web.zoom.us/j/86428207321?pwd=MnM0T3Y0ZE9vR25LbHhQTHBkbVNvUT09 For further details and updates, please see: https://clima.dm.unipi.it/2024/01/22/minicourse-dynamical-systems-algebraic-topology-and-climate/
[15/12/2023] Last lesson before the holiday break. Classes will be resumed on January 9, 2024.
[10/11/2023] FRIDAY November 17: NO LESSON
[10/11/2023] Calendar agreed: TUESDAY 2 p.m. - 4 p.m. / FRIDAY 2.30 p.m. - 4 p.m. AULA N1
[6/11/2023] Preliminary meeting scheduled for November 9, 2.30 p.m. at the Aula Seminari in the Math Department and online (https://us02web.zoom.us/j/86428207321?pwd=MnM0T3Y0ZE9vR25LbHhQTHBkbVNvUT09).
[3/11/2023] The course will be presented on Monday, November 6, at 6.30 p.m. at Aula Magna in the Math Department.
Calendar
The course will consist of 32 hours.
Tuesday: 2 p.m. - 4 p.m.
Friday: 2.30 p.m. - 4 p.m.
Where: Polo Fibonacci, AULA N1
Lessons will also be streamed via zoom: https://us02web.zoom.us/j/86428207321?pwd=MnM0T3Y0ZE9vR25LbHhQTHBkbVNvUT09
References & Course materials
V. Nanda: Lecture Notes of the course "Computational Algebraic Topology"
M. Manetti: Dispense del corso "Istituzioni di Algebra e Geometria", A.A. 2021-22
R. Ghrist: "Elementary Applied Topology", ed. 1.0, Createspace, 2014.
M. Lesnick: "Notes on Multiparameter Persistence", University at Albany, SUNY, 2023
Other resources:
Examination
To be agreed with the teachers. You will be able to choose between seminar and project from a list that will be provided by the teachers.
Contacts
Maria Antonietta Pascali <maria.antonietta.pascali@isti.cnr.it>
Emanuele Delucchi <delucchi.math@gmail.com>
Davide Moroni <davide.moroni@isti.cnr.it>