Combinatorial aspects of persistent homology

Topological data analysis is a tool used to analyze the shape of a given dataset. It allows one to find topological or geometrical features of even large collections of data. Persistent homology is one of the main approaches to topological data analysis in recent times. The strategy is to set some rule to build geometrical objects from data using a parameter given by a real number. As this parameter varies, the geometrical object varies, and persistence homology is the study of the evolution of these objects as the parameter increases.

Recent work aim to expend this strategy to using multiple parameter simultaneously. However, the mathematical models are more complex and further abstract theories need to be developed. This aims to lay foundations that will eventually allow the development of algorithms that can use these ideas in an efficient manner. Our goal is to contribute to this effort, with an approach that is combinatorial and algebraic.

Faculty Supervisor:

Thomas Brüstle

Student:

Partner:

Kobe University

Discipline:

Mathematics

Sector:

Technology; Artificial Intelligence

University:

Université de Sherbrooke

Program: