Algebraic tools for Topological Data Analysis

Topological Data Analysis analyzes the shape of data by topological methods. The main tool is persistent homology. In the one-parameter setting, classical theorems from Algebra allow to associate so-called barcodes, from which one easily reads topological features of the dataset. The multiparameter case is in need of advancing the algebraic tools behind the scenes. In an ongoing project together with Valeria Bertini and Christian Lehn, we are working on a classification of quotients of free multigraded modules using Quot schemes.

In this talk, I give a friendly introduction to Topological Data Analysis and outline how the aforementioned moduli spaces enter the stage.