B0321 - TOPOLOGICAL DATA ANALYSIS

Learning outcomes

At the end of the course, students acquire essential knowledge of geometric and topological methods for practical applications, with a focus on persistent homology and other tools from Topological Data Analysis. They are able to apply topological methods in various contexts.

Course contents

• Review of simplicial complexes and homology
• Discrete Morse theory
• Filtrations. Persistent homology. Barcodes. Structure and stability theorems.
• Topological Data Analysis and Machine Learning. Applications.
• Applications of topology to distributed computing and data visualization.

Prerequisites: basics of algebraic topology, programming and algorithms.

Recommended prerequisite courses: it is strongly recommended to have followed at least the first part of the Algebraic Topology course, up to homology. It is not necessary to have followed the course Introduction to Machine Learning.

Readings/Bibliography

H. Edelsbrunner and J. L. Harer, Computational topology: An introduction

M. Lesnick, Notes on Multiparameter Persistence

V. Nanda, Computational Algebraic Topology Lecture Notes

M. Herlihy, D. Kozlov, and S. Rajsbaum, Distributed Computing Through Combinatorial Topology

Teaching methods

Lectures with blackboard and/or slides.

Assessment methods

Oral exam.

Office hours

See the website of Giovanni Paolini