Winter 2023 Student Projects

HEGL Praktika

Approximate Metric 3D Embeddings of the 3-Sphere

Mentor: Prof. Dr. Christoph Schnörr
Members: up to 5

Description: The topic of this project is to convert subsets of the 3-sphere into finite metric spaces in various ways and to explore structure-preserving 3D Euclidean embeddings for visualization. Besides differential geometry and parametrizations of the 3-sphere, this involves basic techniques from data analysis (multidimensional scaling, graph Laplacians and spectral embeddings; rigid registration of point clouds), numerical optimization and linear algebra, programming and visualization.

Further information: Here.

Persistent Homology and Applications

Mentor: Alexandre Jannaud
Members: up to 3

Description: This project aims to introduce persistence homology and its applications. We will first discover the theoretical aspect and how to implement it through the example of Ribbs complexes for a cloud of points. We will then tackle a more complex application through an example in non-mathematical research (medicine, for example).

Prerequisites: familiarity with the basics of Python and homology