Thematic Einstein Semester on
Geometric and Topological Structure of Materials
Summer Semester 2021
Speaker
Paweł Dłotko (Dioscuri Centre Warszawa)
Title
On the shape of data and relations
Abstract
In this talk we will explore tools of topological data analysis, in particular persistent homology and mapper-type algorithms (including mapper and ball mapper), to explore structure of data. Motivated by a number of knot invariants we will develop new techniques that allow us to use mapper-type algorithms to visualize high dimensional scalar and vector valued functions. We will explore relations of various knot invariants and extrapolate how presented tools may help to compare various, high-dimensional descriptors of materials. We will finalize this talk by showing how the presented ideas can be used to compare different mapper-type graphs of the same dataset. This is a joint work with Davide Gurnari, Anna Jurek, Simon Rudkin and Radmila Sazdanovic.
Contact
tes-summer2021@math.tu-berlin.de