Topological Data Analysis from a representation theory perspective

Abstract: Topological data analysis (TDA) uses topology to identify relevant geometric features of data, such as clusters and loops. This is accomplished by first modelling the data by a family of topological spaces indexed over a poset, and then identifying the topological features that persist over several indices. The field of algebraic topology provides tools to TDA via the language of homology, and persistent homology is the branch of TDA that makes use of methods from representation theory in order to study these representations of posets, referred to as persistence modules.

In this course we will present the basic theory of pointwise finite persistence modules with coefficients in a field. This includes classification results for one-parameter persistence modules where the poset is totally ordered, as well as description of invariants of persistence modules in the multiparameter setting. 

Schedule:
Tuesday October 22, 10.30 – 13:00 aula E
Wednesday October 23, 9:00-10:30 aula C
Wednesday October 23, 13:30-15:30 aula F