Geometric structures are useful in many areas, and there is a need to understand their structural properties, and to work with them algorithmically. The lecture addresses theoretical foundations concerning geometric structures. Central objects of interest are triangulations. We study combinatorial (Does a certain object exist?) and algorithmic questions (Can we find a certain object efficiently?)

This seminar complements the course Geometry: Combinatorics & Algorithms. Students of the seminar will present original research papers, some classic and some of them very recent.

Topological Data Analysis (TDA) is a relatively new subfield of computer sciences, which uses techniques from algebraic topology and computational geometry and topology to analyze and quantify the shape of data. This course will introduce the theoretical foundations of TDA.

This course complements the course „Introduction to Topological Data Analysis“. Students of the seminar will collaborate with students from international universities on concrete projects in topological data analysis or other areas of applied topology.