16:30-16:50 Uhr Lehrprobe zum Thema The Theorem of Carathéodory (auf Englisch)

ca. 17:00-17:40 Uhr Fachvortrag:

Algebraic and Topological Data Analysis

Algebraic analysis investigates linear differential equations with polynomial coefficients by encoding them as ideals in the Weyl algebra D. In this talk, I present several applications of this theory in the sciences. Among others, I present how maximum likelihood estimation - a technique from statistics for the inference of data - can be tackled in terms of D-modules.

The second part of my talk is about the development of algebraic tools for topological data analysis. This area of research extracts intrinsic information of data with methods from (algebraic) topology. The main tool is persistent homology. While the one-parameter case is fully described by so-called "barcodes" associated to the data, one encounters a lack of a corresponding invariant in the multivariate case. I give insights into an ongoing project with Wojciech Chachólski and René Corbet, in which we construct stable invariants for multipersistence modules.