Dates:

• 15.04.2026 - 22.07.2026

Place and Time:

• Lecture: Wednesdays 14:30-16:00; Room: 25.22.00.82
• Exercise Wednesdays 16:30-18:00; Room: 25.22.00.82 

Lecturer:

• Dr. Benjamin Ruppik (benjamin.ruppik(at)hhu.de)

Study programme:

• Master's programme in Computer Science (PO 2015)
• Master's programme in Artificial Intelligence and Data Science (PO 2019, PO 2021)

Credit Points:

• 5 CP (2+2 SWS)

Language:

• English

Content:

• Part I – Mathematical foundations: Basic notions in topology; Simplicial complexes; Homotopy; Simplicial homology; Čech complex & Vietoris–Rips complex; Filtrations.
• Part II – Core TDA techniques & tools: Barcodes & Persistence diagrams; Bottleneck/Wasserstein distances and Stability; Practical TDA software workflows; Vectorization of persistence; Mapper algorithm; UMAP.
• Part III – Topological deep learning: Using topological descriptors in deep learning pipelines; Differentiable/topology-aware components; Topological loss/regularization.
• Part IV – Applications in key domains: Graph learning (GNNs); Natural language processing.